For some fans of “The White Lotus,” watching the show was not enough. They want the full experience.

Last month, Will Potter, an executive at Sotheby’s who lives in Brooklyn, booked a stay at the San Domenico Palace, the Four Seasons resort hotel in Taormina, Sicily, where the show’s second season was filmed.

“There’s very few shows where, as I’m watching it, I’m going, ‘This is so good,’” Mr. Potter, 38, said.

During the first season of the HBO series, which was set in Hawaii, Mr. Potter was especially taken with Tanya McQuoid, the bumbling heiress played by Jennifer Coolidge, he said. As he watched the second season, with his wife, on Sunday nights after they had put their two children to bed, he found himself falling for the show’s idyllic Sicilian setting. Weeks before the murderous finale aired, he had booked a summer family vacation there.

“We were like, ‘This looks amazing, to do a full adventure,” Mr. Potter said. “It looks like a beautiful hotel.”

He added that the family plans to go on side trips inspired by the show’s characters’ forays away from the hotel property. “We were watching the Noto region episode,” he said, “and we were like, ‘What if we mix it up and explore that?’ And then we ended up putting the exact itinerary together.”

The San Domenico Palace, a former Dominican monastery perched on the edge of a promontory overlooking the Ionian Sea, was converted into a hotel in 1896. Its guests have included Oscar Wilde, D.H. Lawrence, Greta Garbo, Audrey Hepburn and Sophia Loren.

After the second season of “The White Lotus” began airing in October, the hotel experienced “a spike in web visits from the U.S. market, and the U.K. and Australia,” Ilaria Alber-Glanstaetten, the resort’s general manager, said. Some of the $4,200-a-night suites are still available in 2023, she added. “Bookings have been affected, but the biggest impact has been on awareness,” Ms. Alber-Glanstaetten said.

Like the majority of “White Lotus” characters, some guests have had stays that were less than tranquil. Elizabeth Taylor and Richard Burton, arguably the most headline-generating celebrity couple of the mid-20th century, became part of San Domenico lore after a dramatic argument on the terrace in 1963. “Liz apparently broke a mandolin over Dick’s head,” Ms. Alber-Glanstaetten said. “The reason for the fight was allegedly jealousy.”

The manager attributes the sometimes stormy mood of the place to Mount Etna, the active volcano that is visible from many of the suites. “It’s hard to describe, but when you are there you really feel it,” Ms. Alber-Glanstaetten said.

Ida K. Mova, 37, a design consultant for Waterworks, a manufacturer of bath and kitchen fixtures, who lives in San Francisco, visited the San Domenico Palace in August. After watching “The White Lotus,” she is up for a second trip. “I can’t wait to go back,” she said.

The online travel giant Expedia calls the trend of television- and film-related tourism “set-jetting.” Nearly two-thirds of travelers who took part in a recent survey reported having booked a trip inspired by a movie or TV show, the company said.

The first season of “The White Lotus” was filmed at Four Seasons Resort Maui at Wailea in Hawaii. Like the San Domenico in recent months, that hotel had a spike in reservations last year, but it was hard to tell if it was because of the HBO series or because the pandemic lockdown had lifted soon after it aired.

“We strategically wanted to try and reopen after the filming had been done,” Robert Delaney, the resort manager at the Four Seasons Maui, said. He added that many guests ask about the Pineapple Suite, a room that exists only in the “White Lotus” universe, and the most ardent fans “talk about little intricacies of the characters in the show.”

Mike White, the creator of “The White Lotus,” has not always portrayed hotel staff members in the most flattering light. In the first season, the manager, Armond, went on a drug binge and had sex with another staff member in his office. In the second season, Valentina, the manager of the Taormina resort, makes use of an unoccupied suite to have a fling with a prostitute.

Mr. Delaney said he found the depictions of hotel workers to be lacking in accuracy at times. “The portrayal of some of the activities that the characters or the managers took part in was not a fair portrayal of what the everyday role is for someone like me, for example,” he said.