We launched and then paddled along the deserted shoreline. Habitation pretty much stops at Nerano, but the coast keeps going until it makes a 180-degree turn toward Sorrento. Eventually, Federico and I found ourselves floating right at the tip of the Sorrentine Peninsula. In front of us was a channel of water, and beyond it Capri. We looked both ways, then crossed. The journey isn't dangerous, but it is scary—mainly because the ocean liners in the distance look as though they're heading straight for you.

Halfway across, we stopped for a drink. Behind us, the mainland seemed far away, yet Capri looked no closer. A little more than an hour after leaving the mainland, we had arrived at an enormous limestone wall. It was so tall we had to tilt our heads all the way back to see the top, where someone had managed to perch a very pretty house. At the Faraglioni, we lined up behind the tour boats, which were passing through the arch one by one before heading back to pick up a new load of passengers and do it all over again. Then it was our turn. We paddled through the arch. Underneath, it was dank and dark and all sound ricocheted. We paddled through and back into the light, then turned around and did it again.

The beach at Capri's Marina Piccolo was a carpet of white pebbles. As we pulled in, a school of tiny fish did a half-moon jump in front of us and disappeared into the crystalline water. We stored the kayaks at a beachside bar with a man who asked, "You paddled all the way from Nerano?"

If Hollywood ever makes another movie that is set in heaven, they would be wise to shoot in Capri. The streets are narrow and meander in apparently senseless directions. Getting lost is inevitable, but no one seems to mind because each unfolding streetscape is more exhilarating than the last. The island, which is essentially a big hunk of limestone, periodically flattens out, and this is where the houses are—nestled amid towering pine and palm trees, and nuzzled by roses and cypresses.

The taxis are all convertibles, and as conventions go, this is a noble one. On sunny days, the drivers stretch a swath of canvas over the top called a tendalino, so the passengers are shaded but aerated. From the top of the island, the view stretches all the way to the Gulf of Naples, with the buildings of Naples curled around the beach and Vesuvius standing guard behind. Sorrento is to the right, and it sends out ferry after ferry loaded with visitors bound for Capri.

At my hotel, the proprietor—a pleasant Italian who appeared to be aging in exquisite taste—could remember how it was back in the 1950s: At the zenith of the holiday season, four boats a day came to Capri. Like many locals, he runs his hotel during the summer and returns to his fishing boat for the winter. I told him about yesterday's mackerel, and he said, "Ah, sgombro." He then fixed me with a serious expression and asked, "You didn't paddle all the way to Capri, did you?" I told him that we had. He considered it an impressive accomplishment.