One of our first infractions at Ghibli Park was hoisting our 1-year-old onto the polyester tummy of a woodland spirit creature. Another was letting him slip under a barricade and shelter inside a furry bus with cat eyes for headlights.

“He’s not following the protocol,” I told my wife, as the staff overseeing the cat-bus play zone looked on anxiously.

“He’s making a mockery of it,” she said. But we didn’t stop him.

Ghibli Park, which opened in November outside Nagoya, Japan, pays homage to the eccentric, enchanting films of Studio Ghibli, a company co-founded in the 1980s by the director Hayao Miyazaki. We took our two toddlers there because their favorite movie is “My Neighbor Totoro,” a beloved 1988 Miyazaki film starring the spirit creature and its cat-bus sidekick.

As parents, we thought it would be fun for our boys, 3 and 1, to experience a “Totoro” immersion. And as longtime Ghibli fans, we were keen to see what the place looked like.

American visitors may wonder how Ghibli Park compares with Disney World. It doesn’t really. It feels much lower-key and has no rides, exotic animals, jumbo turkey legs or animatronic American presidents, among other things. The main point is to wander around soaking up Miyazaki vibes.

Also, the park is not finished. Grafted onto an existing municipal park, it opened late last year, but as of early July only three of five planned ticketed sites were open. When I booked for a June visit, tickets to only one of those sites — a building called “Ghibli’s Grand Warehouse” — were available to international visitors reserving through the park’s website. (It was possible to book the other two sites through Japanese travel agencies, but I only learned that much later, from a Japanese speaker.)

Susan Napier, a biographer of Mr. Miyazaki at Tufts University who visited Ghibli Park in April, told me that it had struck her as a “work in progress.” She also described the ticketing process, which has included lotteries and long online queues, as “byzantine and not fun.”

Maybe this is why Studio Ghibli itself seems ambivalent about promoting Ghibli Park. In Japan, it has run advertisements advising fans to “take your time” visiting.

A hypothetical theme park celebrating Nintendo or Pokemon, two other iconic Japanese creative brands, would almost certainly feel more Disney World-like, said Matt Alt, the author of the 2021 book “Pure Invention: How Japan’s Pop Culture Conquered the World.” But he added that the park’s diffuse layout and low-key marketing were in character for a studio co-founded by Mr. Miyazaki, a director who has never hidden his anticapitalist politics.

Ghibli Park is not a place to “turn your brain off,” Mr. Alt told me. “It demands a level of intellectual engagement that most parks do not.” When I booked our visit, in March, a bit of mental stimulation sounded nice. I imagined wandering the grounds in dappled sunlight, musing on Mr. Miyazaki’s cinematic oeuvre as our boys paused to collect acorns — just as the two sisters who star in “Totoro” do. (The boys, who are Anglo-American, love the acorn scenes so much that they learned the Japanese word for the nut, donguri, before the English one.)

In reality, we arrived just before our three-hour afternoon visiting slot at Ghibli’s Grand Warehouse, and our intellectual capacity was limited. Our parental nerves were fraying from the hourlong journey from Nagoya and the general struggle of moving tiny, diapered humans around an unfamiliar place.

Our morning in Nagoya had already been tarnished by a 4 a.m. wake up and some public displays of unchecked toddler emotion. On the grounds of the 17th century Nagoya Castle, for example, our 3-year-old, nicknamed T, burst into tears when he learned that the castle was closed for renovation.

To break his mood, we took the emergency measure of buying him and his brother, nicknamed B, ice cream cones as a second breakfast. That stopped the crying, but our mounting fatigue had raised the stakes for our visit to Ghibli Park. Would the trip to meet our favorite magical creatures make all the time, money and energy that it entailed worthwhile?

Ghibli Park may see a bump in domestic tourism this summer because Mr. Miyazaki released a new film in Japan this month. But, for my family, making a pilgrimage there was all about seeing Totoro and the cat bus.

“Totoro” follows the two sisters, Mei, 4, and Satsuki, 10, as they settle into a spooky house in the Japanese countryside with their father, an archaeologist. Their mother is stuck in a nearby sanitarium, suffering from an undisclosed illness.

After Mei meets Totoro by stumbling into its lair inside a giant camphor tree (and falls asleep on its tummy), she and her sister encounter the creature a few more times and learn more about its magical powers. Eventually, as their mother’s condition appears to worsen, they call in some very important favors from Totoro and the wild-eyed cat bus.

Professor Napier told me that “Totoro” illustrates an aesthetic that runs through the Ghibli catalog, and which tends to be more ambiguous and subtle than Disney’s. She described it as “the immersive, low-key magic of being a human being connected with other things.”

“It’s a world that you like,” Professor Napier, who is writing a book comparing Ghibli with Disney, said of Mr. Miyazaki’s animated universe. “But it’s also full of the unexpected and complex, and sometimes scary.”

Totoro and the cat bus can indeed be a little frightening, especially when they flash their teeth. But the movie is much sweeter than it is scary. It’s set in “a time before television,” as Mr. Miyazaki once told an interviewer, and infused with sublime, hand-drawn pastoral imagery — pastel sunsets, a snail crawling up a plant stalk — that makes you want to be a kid growing up in rural idyll.

The film also celebrates a child’s sense of wonder. Mr. Miyazaki created “Totoro” with kids in mind — he said he hoped it would make them want to pick acorns — and many critics have seen it as an ode to childhood innocence. It’s no accident that Totoro and the cat bus are visible only to the sisters, not adults.

Maybe this is why I still cry every time I watch the final credits roll: “Totoro” reminds me that my boys will never be this young or innocent again.

In our Seoul apartment, they play with Totoro and cat-bus dolls, sleep in Totoro pajamas and sit on a Totoro potty. Their fandom is so intense that my mother-in-law bought us tickets to a “Totoro” stage adaptation at the Barbican Theater during our last trip to London.

In Nagoya, before we left for Ghibli Park, B demonstrated his enthusiasm by bringing a plastic cat bus to the hotel buffet — and feeding it a breakfast of whipped cream. He also showed the toy to a man in a ninja costume who posed for a selfie with us outside the castle.

The ninja cracked a knowing smile, indicating that he, too, was a “Totoro” fan. “Cat bus,” he said in Japanese, as if the phrase were a code word.

Ghibli Park lies in Nagakute, a small city in the hills outside Nagoya, a few stops down a highway from an Ikea. There’s no Ghibli entrance gate, exactly; you just wander into an unremarkable municipal park and look around for the Ghibli sites for which you have reserved tickets months in advance.

The Grand Warehouse is a sleek, multistory building the size of a modest mall or sports arena, with plenty of sunshine streaming in through skylights. It sits near a grassy lawn, an ice rink and some future Ghibli sites that are under construction.

Inside, there are replicas of structures from the films, including the towering bathhouse from the Oscar-winning 2001 film “Spirited Away,” and dozens of made-for-Instagram tableaux of Ghibli scenes and props.

The attention to detail is striking. In an area devoted to the Ghibli film “Arietty,” I saw a giant drop of plastic dew affixed to a giant fake flower, for example. Nearby was an intricately detailed replica of the castle from “Howl’s Moving Castle,” my older son’s favorite Miyazaki film after “Totoro.”

“The castle, daddy!” Three-year-old T said with delight. At last, a Japanese castle that didn’t make him cry.

The problem was that most of the tableaux were mobbed with Ghibli fans — and lines that we didn’t have time to stand in with restless toddlers. The building’s only restaurant was similarly oversubscribed. We eventually found a kiosk advertising cake, but the staff said that the cake had run out.

After about an hour of canvassing the warehouse, we headed for “Children’s Town,” a play area devoted to scenes from “Totoro” and other Ghibli films.

Children’s Town has three rooms. The first is a labyrinth combining scenes from more Ghibli films than I could count: The orange train from “Laputa: Castle in the Sky,” the bakery from “Kiki’s Delivery Service” and so on. The boys loved it, even if daddy thwacked his head following them through a crawl space.

The other rooms were devoted to “Totoro” and had mercifully higher ceilings. There was the house where Mei and Satsuki live with their dad. Over there was the camphor tree, where a giant Totoro lay regally beside some oversize donguri. And in the far corner sat the majestic, furry cat bus.

It all looked fun, kid-friendly and immersive — almost, in fact, like something you’d find at Disney World. The boys were in heaven.

“Toe-toe-row! Toe-toe-row!” B said, standing inside the tree, with the same intonation as the movie’s rousing, marching-band-style theme song.

“Hey, Totoro!” said T, who had been carefully inspecting the giant acorns. “Wake up!”

But even though Children’s Town seemed designed to nurture the child’s sense of wonder that Mr. Miyazaki celebrates in his movies, the warehouse staff informed us of several rules that dampened the vibe. Notably, it was forbidden to put children on Totoro’s plush tummy, or to allow them to play inside the cat bus zone for longer than three minutes — even if the zone was not crowded, which it wasn’t.

The staff members were friendly, but their rules made little sense for kids as small as ours. I wondered if that was another sign that Ghibli Park was still a bit rough around the edges. Take your time visiting, as the studio says.

We grudgingly agreed to the no-tummy policy, but B wished to play nowhere else but inside the cat bus. We were with him. We had spent several months — a good chunk of his life! — waiting for this moment.

The staff, sensing our resolve, suggested a compromise. A special time extension could be granted under the circumstances, they said. Rather than the usual three minutes, our B could have six.

Make that nine. Then 12. Et cetera. At 5 p.m., he was among last, and smallest, Ghibli fans to leave the building.

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Last summer, on an overcast July day, the coastal town of Sitka, once the capital of Russian Alaska and long a popular stop on Inside Passage cruises in Southeast Alaska, was thronged with passengers disembarking from three cruise ships. To accommodate the crowds, the city had closed the main street to cars. In their place, food trucks, carts and stands had popped up, creating a festival atmosphere where ambulatory diners spooned seafood chowder and gobbled tacos.

“In summer, street food seems like the way to go in a place like this,” said Gretchen Stelzenmuller, who cooked professionally in San Francisco before moving back home to Sitka during the pandemic and opening her mobile food business, Enoki Eatery, which serves Japanese-inspired comfort food. “It’s healthy and uniquely celebrates Alaska ingredients, but you can also roll in and grab a bite and still do your tour.”

In the wake of the pandemic, as cruising returns to full strength in Alaska, food trucks and other vendors have proliferated in ports from Ketchikan to Seward.

“With a food truck, you can get into the restaurant business without the full brick-and-mortar entrepreneurial costs,” said Jon Bittner, the state director of the Alaska Small Business Development Center. “That’s pretty attractive in smaller communities that service cruise ships.”

For passengers with only a few hours in port and lots to see — including ferry riders taking the Alaska Marine Highway — food trucks offer local flare at relatively reasonable prices and in less time than full-service restaurants.

“Food trucks are a natural extension of what draws people to Alaska, being outside,” said Aaron Saunders, the senior editor at Cruise Critic.

Expect to pay a little more than in the Lower 48, given the high cost of living. Last summer, I bought a chicken and rice dish for $16 from a stand in Seward, a few dollars more and a free can of Pepsi less than the equivalent truck fare in New York City.

For the 2023 cruise season, which generally runs April to October, Alaska cruise authorities expect 1.65 million cruise passengers, up from the record of 1.3 million in 2019. Most will sail the Inside Passage, a roughly 500-mile route in Southeast Alaska that weaves through islands protecting it from the churn of the Pacific Ocean.

While ship-bound visitors may make their way through Anchorage — which has its own thriving food truck scene — the following popular cruise stops form a locally grown coastal culinary trail.

Ketchikan: Shrimp and grits and fried chicken sandwiches

Often the first call in Alaska for northbound Inside Passage cruises, Ketchikan — a traditional Tlingit fishing camp that today thrives on tourism, commercial fishing and forestry — booms with the arrival of cruise ships. Passengers disembarking for day trips in the Tongass National Forest or to see the totem poles at Saxman Native Village will find a few food stalls among the vendor booths on the cruise dock — including D’s Fish and Chip Shack — while more robust food-truck offerings can be found within walking distance.

“If you want to see someone make out with a chicken sandwich, come by our truck sometime,” wrote Thane Peterson, the owner of the food truck Chicke Chicke Bang Bang, which specializes in chicken sandwiches ($12), in an email. He described diners with “eyes closed, groaning, mumbling ‘Oh my god.’”

The truck, which launched last year, can often be found parked near the cruise docks, and passengers, Mr. Peterson said, account for two-thirds of annual sales.

A few blocks from the cruise berths, Amber Adams aims to open the town’s first food truck lot, Dock Street Yard, in August with room for three vendors.

After moving to Ketchikan from New Orleans four years ago, Ms. Adams found herself cooking Creole dishes with Alaskan ingredients as both a reminder of home and a necessity in a small town with few dining options. Currently the only tenant on the lot, her business, the Food Truck, will serve shrimp and grits ($15) and rib-eye banh mi po’ boys ($18).

“Starting a restaurant is scary,” Ms. Adams said on a break from prepping her truck. “But it’s a different beast here because of the huge influx of people for six months that basically doubles the population in town.”

Sitka: Smoked salmon musubi and seafood chowder

In the high season, disembarking passengers can match Sitka’s population of about 8,500. Again this year, the city is restricting the main thoroughfare, Lincoln Street, to foot traffic on days when cruise ship capacity in port exceeds 5,000, inviting mobile businesses to set up.

“I think it’s a really great way to showcase all the talent in this town,” said Ms. Stelzenmuller, who launched Enoki Eatery last year as a Lincoln Street pop-up serving variations of Hawaiian-style musubi, a wedge of rice topped with Spam or fish and bound by a seaweed wrap. “Street food should be a reason to come here.”

This year, she purchased a food truck and parked it downtown. The vehicle has allowed her to expand the menu, which may include steamed buns stuffed with pork or salmon and cream cheese ($9) and smoked salmon musubi ($8.50).

Just off Lincoln Street, behind Ernie’s Old Time Saloon, Barbara Palacios serves poke, chowder and ceviche from her cart, the Fresh Fish.

“We’re having a food-truck boom here in Sitka,” said Ms. Palacios, who plans to upgrade her vehicle later this year to a full-size food truck and continue offering poke (tuna or salmon, $18), halibut ceviche ($14) and seafood chowder ($9 a cup, $14 a bowl).

“It’s a labor of passion and love,” said Ms. Palacios, who often works 12 hours a day in season.

A few blocks east, past the Russian Orthodox St. Michael’s Cathedral, Ashley McNamee runs Ashmo’s, serving locally caught fish in smoked salmon macaroni and cheese ($9), black cod on coconut rice ($10) and lingcod sandwiches ($12).

Like many food truck operators here, Ms. McNamee, whose résumé includes 14 years cooking at an Alaskan fishing lodge, chose the food truck over “the restaurant grind.” Still, she added, “With the influx of people off cruise ships, it’s almost all I can do to keep up.”

From the center of town, it’s a little over a mile to Harbor Mountain Brewing Co., where Cambria Goodwin and Luke Bruckert base their brick-and-mortar Campfire Kitchen, a wood-oven pizza specialist. This year, they’ve added a mobile kitchen at the site to prepare fried chicken sandwiches ($15) and fried cheese curds ($9) to keep up with the crush of business.

In a separate endeavor, Ms. Goodwin recently opened Sitka Salmon Wagon, serving salmon bisque ($10 a cup, $16 a bowl) from a trailer parked downtown “to feed the masses,” she said.

The weather can be a challenge to outdoor dining in Southeast Alaska’s temperate rainforest. After one year running Blumen Dogs hot dog cart, Shawn Blumenshine is adding a food truck and will operate in several locations, serving Nathan’s Famous franks ($7) and creative versions ($11), including the Banh Mi Dog with carrots, cabbage, jalapeños, vinaigrette and sweet chili sauce. To date, patrons are largely local. “I’ve got hardcore banh mi fans,” said Mr. Blumenshine.

Juneau: Fish tacos and potato pizza

The state capital, Juneau, is no stranger to food carts and trucks. Trailblazers in town include Bernadette’s, a Filipino barbecue cart started in 1996 that draws lines of visiting cruise ship crew members, many of whom are Filipino, and Pucker Wilson’s, opened nine years ago, and dishing two-fisted burgers like the Huskey Dawson topped with bacon, onion rings and cheese ($16).

Visitors looking for Alaskan seafood on the go will find it a few blocks from the cruise pier at Deckhand Dave’s, a fish taco purveyor that anchors a food-truck yard. The truck and yard are run by Dave McCasland, a self-taught chef who worked for two years as a cook on a commercial fishing boat to pay off his college loans before launching his truck in 2016 with items like blackened rockfish tacos ($13.50 for three).

In 2019, he developed the food truck lot with room for the original business, a spinoff oyster and champagne bar and other mobile tenants, today including the Alaskan Crepe Escape and a cotton candy maker.

“People travel for a taste of place, and when they come to Alaska they really want to eat seafood and eat local,” said Midgi Moore, who runs Juneau Food Tours, guiding visitors to places like Deckhand Dave’s.

Five miles from downtown, in the direction of the Mendenhall Glacier, the Alaskan Brewing Company tasting room hosts food trucks, including Forno Rosso, serving wood-fired Neapolitan-style pizzas ($13 to $17 for 10-inch pies). Before moving to Juneau, the truck’s owners, Alexander and Kym Kotlarov, lived in Rome where they developed a passion for pizza that led to the mobile business named for their red-tiled oven.

If visitors find out-of-the-way Forno Rosso, they tend to be independent travelers or craft beer fans, according to Ms. Kotlarov, who uses specialty flour, San Marzano tomatoes from California and locally grown Genovese basil.

“I feel like we’re swimming upstream with our agenda of caring about quality and staying true to the Italian thing,” Ms. Kotlarov said, noting that she continues to offer Italian potato pizza as a special periodically.

Seward: Reindeer hot dogs and birria plates

A port on the Kenai Peninsula, roughly 130 miles south of Anchorage, Seward tends to get cruise ships at the start or end of their itineraries. On the road system, it also draws travelers by land.

“They disembark and embark in Seward,” said Kameron Weathers, the owner of Wild Spoon food truck and catering company. “We’re not a stop.”

Still, ship crew and road-trippers patronize her stand for souped-up reindeer or buffalo dogs topped with beet kimchi and ginger aioli ($10), and venison specials.

In summer 2020, despite the collapse of tourism during the pandemic, Faith Alderman and Fiona Crosby launched their breakfast-and-lunch business, the Porthole, to capture the early morning traffic at Seward Harbor with breakfast burritos ($12) and English muffin sandwiches ($8). Open at 4:30 a.m., the business draws captains, deckhands and visitors taking boat trips to the nearby Kenai Fjords National Park.

Seward travelers bound for Alaska SeaLife Center, an aquarium and marine research center on Resurrection Bay, can’t miss Los Chanchitos, a busy Mexican food truck that anchors a nearby lot shared by Early Bird coffee truck and an ax-throwing business. It specializes in birria or beef brisket tacos ($17), among other fare.

Peter Cavaretta, who spent more than a decade in the southern Baja Peninsula, opened the truck last April after visiting his sister in Seward and seeing “lines out the door for semi-average food at high prices,” he said. “I wanted to do super-good food at moderate prices.”