The aperitifs arrived as the Capri sun dipped into an orange band across the Gulf of Naples and a couple on the terrace talked about how quiet the island had become. The hotel felt empty, and its barman, in elegant suit and tie, interrupted his revelry about the prepandemic days to shoo off a sea gull deprived of its usual tourist-scrap banquet.

“The birds,” the barman explained, “are famished.”

After more than a year of lockdown, the Italian islands off Naples are also hungry for visitors and a return to the bustling summer seasons that are their economic lifeblood. In May, glamorous Capri, that Italian Epcot of jet-set dreams, and its smaller, gritty sister, Procida, which feels like a neighborhood of Naples drifted out to sea, had managed to become among Italy’s first fully vaccinated islands. Prime Minister Mario Draghi urged travelers “to book your holidays in Italy.”

Those travelers who do have a chance of hitting a rare, perhaps once-in-a-lifetime sweet spot in which thinner crowds, wonderful weather and more motivated, vaccinated hospitality make for memorable stays. To be on the islands these days is to be present for the stirring of great beauties who, having slept late, are fully rested, rearing to go and full of aspirations about what the future might hold.

But the two islands want very different things. On Capri, luxury restaurant and hotel owners thirst for a return to V.I.P. normalcy, while some residents hope a momentary relief from the cruise ships might trigger a re-appreciation of the island’s biodiversity and local culture. On Procida, where the 17th-century pastel-colored fishing village has served as the picturesque Italian postcard backdrop for movies like “The Talented Mr. Ripley” and “Il Postino,” locals are both hopeful and wary that their inoculations and a surprise designation as Italy’s Capital of Culture for 2022 will thrust them into the upper echelon of southern Italian destinations.

Yearning for authenticity

Despite having over time visited nearly every corner of Italy, I had never been to either. Capri’s crowds and schlock-and-awe reputation scared me off. Procida was eclipsed on my radar by its larger neighbor, Ischia. But their Covid-free status, proximity to my home in Rome, and need to get away after a brutal year all added up to it being time to go.

On that first night in Capri, my wife and I walked along winding bougainvillea-perfumed paths devoid of luxury shoppers and Limoncello-buzzed crowds. We looked nervously at all the shuttered restaurants and the clocks on our phones. Back then, curfew still fell over the island and all of Italy at 10 p.m. Like the sea gulls, we were hungry.

In the center of town, we followed some voices around a corner to the Hangout pub. Locals talked about school, and children ran around. We reluctantly ordered burgers and, as if characters in a Patricia Highsmith story, bumped into friends from Rome whose romantic getaway had turned into a reckoning over whether he cared more about her or his sailboat. Then their friend, the son of an Italian diplomat who had summered at his family villa in Capri for decades, turned the corner with his wife. We were suddenly a pod.

“Capri is coming back different, stronger,” Lorenzo Fornari, the Capri veteran, explained to me. He spoke rapturously about the Zagara orange blossoms growing atop the island’s towering Mount Solaro that he uses to flavor Solaro, the artisanal gin he had started making with local farmers.

A couple of days later I visited him in his terraced garden filled with kiwis, figs, lemons (one of which he plucked from a tree and used as a map to explain the island’s geography), wild fennel, even banana leaves.

“I swear,” he said. “Everything grows on this island.” A test batch of the spirits had just arrived from the distillery, and he dropped a sprig of rosemary into a glass of it before a final taste test. He approved and talked about how Capri needed more such sustainable projects, and how he worked with local artisans and a cooperative of farmers in Anacapri, the much larger, and less polished, part of an island, which, he said, had “a lot to offer.”

An exorbitant taxi ride across the island brought me to Anacapri, where a line of schoolchildren in uniform wished “buon appetito” to the people lunching in the garden of Gelsomina, one of the first spots on the island to serve the famously airy caprese ravioli, cheese-stuffed pasta sweetened with their garden’s tomatoes. As a waiter explained to a lone group of tourists that the island was usually overcrowded, his sister, Gelsomina Maresca, said “We are hoping that the Americans come back.” Just not too many of them, she added, as her mother cut baby artichokes in the kitchen. “Anacapri is getting bigger but we hope it will never arrive at the level of Capri. It’s too commercial. We’re authentic.”

Authenticity, of course, means different things to different people. Others in the fashionable center of the island argued that tourism and hospitality, starting with the Emperor Tiberius 2,000 years ago, was in Capri’s blood and that, for all its natural beauty, the island was not without its prodigal guests.

“What a pleasure to hear from you,” Nicolino Morgano, 64, the owner of the Scalinatella, a sumptuous boutique luxury hotel, said into the phone behind his front desk. He promised the return customer her usual room and impeccable service. Capri, he said to the woman on the phone, “is ready to give you the usual emotions.”

“People keep calling and saying they are coming and that “I want my table,” said Francesco De Angelis, 55, whose family owns the venerable La Capannina restaurant. Days before reopening, four generations of the family, all vaccinated, sat in their quiet dining room, surrounded by clean glasses, photos of famous patrons such as Dustin Hoffman, and told stories about others, including Michael Douglas and Kirk Douglas, before him. They could feel Capri’s energy coming back.

“It’s joy, joy, joy,” Mr. De Angelis said.

‘The year of rebirth’

Italy’s culture ministry also had reawakening in mind when it chose nearby Procida, a low-slung volcanic island of nearly 4 square kilometers (about 1.54 square miles) and 10,000 people, as 2022’s Capital of Culture. Procida would “accompany us in the year of rebirth,” the culture minister said in a decision that prompted what the Procida mayor, Raimondo Ambrosino, told me was an “explosion of joy.”

Mr. Ambrosino, who was an extra in “The Talented Mr. Ripley,” said Procida, the first island in Italy to be fully vaccinated, had planned a dense schedule of cultural events that included the “regeneration” of abandoned places. The ruined 16th-century Palazzo D’Avalos, which in 1830 became a prison that ultimately held some of Italy’s most hardened criminals until it closed in 1988, would become a cultural center. The old lighthouse could be a museum about the surrounding sea life. The old medieval walled Terra Murata town at the northern tip of the island, where the Abbazia San Michele Arcangelo features a Nativity scene made from shells, could be spruced up.

But really, he said, they had no intention to make any big changes.

“We don’t have to do anything new,” Mr. Ambrosino said as he reclined in the shabby City Hall against an open window facing the sea. Maybe the national attention, government funds and additional tourist dollars could be used to refurbish the island’s many ruined buildings into new Airbnbs, he said, but there wasn’t any appetite for luxury hotel complexes. “They tried to build one once,” he said. “And it came to a bad end.”

If Capri is stained by decadence, Procida is marred with decay. But there is a Havana-like romance to its shabbiness, to the fallen plaster caught in chunks by nets above the altars or dusting the seats in the churches, to the older women with their forearms folded on windowpanes as they stare motionless at the sea, to the gray blotches left by disintegrating pastel facades that are like a Rorschach test on what type of Italy you see here. Is it run down or the real thing? Something to move beyond, or to keep at all costs?

Procida doesn’t seem sure either. The mayor acknowledges that the culture award would draw more tourists, but he says there are only so many ferries to bring them, and that the island nominated itself so that it could stay the same and “to tell our young people about our past so that they would understand they had a future.”

He saw Procida’s past, present and future as an authentic story of a seafaring people, where native sons, as they had for centuries, become fishermen and cruise and merchant ship captains. After long and often well-paid spells at sea, they would return to wild, almost imperial, gardens, fragrant with the lemon trees planted by their mariner ancestors who harvested citrus to fight scurvy at sea. But now those inhabitants favored oranges and apricots, angel’s trumpet flowers and broom. On land, they stroll unbothered down treacherous streets without sidewalks but filled with Vespas sputtering under portly drivers, tiny Ape trucks making deliveries of concrete, and hundreds of the whizzing electric bicycles, equipped with a little seat for a child or groceries, that have become the preferred mode of transportation.

“If anything,” Mr. Ambrosino said, “the Capital of Culture puts us too much in view.”

The last thing its locals wanted were crowds of tourists visiting discos, pubs and luxury boutiques to clog things up. God forbid anyone suggested they open up a tourist trap to sling coffee. “They want to be the guests. That’s why the rhythm is what it is. There’s no rush.”

Winding staircases, noisy roosters

But there was a rush for me. If the lack of crowds on Capri opened a brief window to see the big island as it once was, I wanted to see, and I wanted my children to see, Procida before the crowds came, before it disappeared and became, despite all the local resistance, another Capri.

In that regard, it did not disappoint. The window of our modest Airbnb was decorated with a typewriter because it was purportedly where Elsa Morante, the great Italian author, wrote her 1957 novel, “Arturo’s Island.”

“The Procidans are surly, taciturn,” Morante observed, adding, “The arrival of a stranger arouses not curiosity, but rather, distrust. If he asks questions, he is answered reluctantly because the people of my island don’t like their privacy spied on.”

All I spied through the bedroom window was a brood of hens and an incessantly noisy rooster, perched on the high branches of an orange tree. A path through the garden’s lemon groves led to a dilapidated outlook, its plaster of painted vines faded and fallen, that looked out onto the dark Chiaia beaches. To get to them, we walked through narrow alleys, down winding metal staircases or old concrete stairs as steep and straight as sluices.

We took an affordable boat ride around the island, with a stop for a dip in the cold, clear sea. To be honest, it was much less spectacular than a similar ride around Capri. There was no Blue Grotto. The Faraglioni of Procida are mere pebbles compared to the majestic rocks of Capri. The skipper in Capri had pointed out the cliff above which the Emperor Tiberius lived, and the Casa Malaparte, a favorite of fashion houses, which “doesn’t have paintings because the windows are the paintings,” he said. In contrast, our skipper in Procida shook his head at a concrete block with two tiny windows atop a small rise of Mediterranean scrub. “A squatter’s house, built overnight,” he said. “A travesty.”

At the Corricella fishing village, we grabbed fresh orange and lemon juice from La Locanda del Postino bar, where the movie was filmed. The mounds of white and brown fishing nets and lingering, leathery old men looked like props for another film. But the two fishermen bickering with one another for leaving a bucket on their boat were not acting.

“The people are going to go nuts,” said the chef at Caracalé when he finally inspected their haul of cod.

The food all over the island — from the cream-filled pastries in the form of ox tongues for breakfast to the nespolino nightcaps made from the seeds of loquats — is memorable, and compared to Capri, much more affordable.

At Caracalé, the bean and mussels soup was so good I asked if the mollusks floated in butter. (“Cream from the beans,” the waitress explained, looking at me like a crazy person.) At Da Girone, where the eponymous white-bearded owner danced with customers while his daughter took orders, the spaghetti with lemon pesto and mussels nearly distracted us from the sunset and the views of Ischia and Procida’s Vivara natural reserve, connected to the island by a small causeway that frustrated cyclists with a locked iron screen. At La Conchilglia da Tonino, the Speedo crowd walked in off the ashtray-colored sand for raw fish and pastas flavored with sardines and green peppers.

“We’re hoping that being the Capital of Culture will change things for the better,” said Sabrina Bevere, 28, a waitress at the restaurant. “We want Procida to come back stronger, and no longer be considered a minor, second-rate island behind Ischia and Capri.”

There are already a few charming boutique hotels. There’s, gasp, glamping. But change does not come easy here.

“We’re scared,” said Nunzia Frontino, 86, whose ground floor house opened right onto the Corricella harbor. She spent the morning standing on her small porch, looking out at the port through a pair of hanging pants set out to dry. She remembered when there was only one cafe, when the port was purely for fishing, when the sand stretched farther into the gulf. Now more modern aperitif bars offering artisanal beer and pink lady cocktails had opened up. A store with fabrics from India and an outlet in Rome sold dresses and bags. The pandemic had momentarily frozen things in place, but the summer, and the big year to come, promised to bring a transformative thaw. “I’m not going anywhere,” Ms. Frontino said defiantly.

Even Mr. Ambrosino, the mayor, seemed reluctant about talking up his town too much. Asked for recommendations on especially attractive spots to see, he shook his head.

“If they are our secrets, we have to keep them,” he explained. “You have to lose yourself here.”

That wasn’t hard to do. One evening, on the way to dinner, Google Maps led us astray as the side-view mirrors of Vespas, Fiats and electronic bikes nearly clipped us along the main road. We followed our phones into a warren of streets, and realized, with the help of locals who told us that we were lost, that we were indeed lost.

We finally found the Pergola restaurant, but it sat across the private property of a man with a famously grumpy reputation, judging from the reaction of the locals when he appeared. The driver of a taxi who stopped to offer us a ride actually hid behind his car door. But we explained our predicament to the landowner, and he grudgingly opened the gates of his property and led us toward the restaurant outside his back gate. Before letting us out, he took a quick detour to his garden of lemon trees. He hopped up and plucked one, as big and lumpy as a gnarled Nerf football, and gave it to my son.

He still has it.

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