Ms. Brown sympathized with the criticism of day-trippers.

“I understand how they feel,” she said. “I hate the football traffic in Iowa City, too. But you get what you get. If you live by tourism, you die by it.”

Visitors like the Browns rarely have enough time to find the good places, since many of those require daunting hikes that don’t fit into short schedules, like the 777 steps up the Scala Fenicia, a staircase over the mountain to Anacapri.

The hike is like climbing a 60-story building. But at the top is the magnificent Villa San Michele, now a museum with a cafe supporting vertiginous rooftop views of the Bay of Naples and the port of Capri 1,000 feet below.

Mr. Esposito sometimes guides visitors to the Passetielo, a hard-to-find trail up the cliff face of Monte Solaro, which physically separates Capri from Anacapri, and offers beautiful vistas. “You almost never see anyone else up there,” he said.

“This is the good thing about Capri,” said the town’s tourism chief, Antonino Esposito, a distant cousin of Luigi. “Even in the high season there are places you can go and no one sees you. You can always find the Capri you want.”