Capri's marvelous waters afford great swimming, which you can easily do from one of the small but picturesque local beaches. Most are organized by paying beach clubs (stabilimenti balneari), which will provide you with a changing cabin, towels, and a deck chair for about 15€ per day; they are usually open mid-March to mid-November, 9am to sunset. Bagni di Tiberio is a nice, sandy beach on the north side of the island, near the ruins of a Roman villa. The beach is only about 1km (a half-mile) from Marina Grande, but getting there involves a steep and rocky descent that can be arduous on the return leg. We recommend going by boat instead -- you can get passage there and back for 6€ from Marina Grande.
You'll find two more nice beaches in Marina Piccola, on the southern side of the island. To the east of the village is Marina di Pennaulo, and to the west is Marina di Mulo; both were a favorite haunt of the 1950s and 1960s jet set. The only other beaches on the island are a small one by the Blue Grotto (Via Grotta Azzurra), one by the Faro (lighthouse), and one by the Faraglioni (Via Tragara).
We also recommend a boat tour of the island. You can hire a private boat, with or without a mariner, from both Marina Grande and Marina Piccola, or board a tour.
Even if you are only moderately fit, do not miss the opportunity to hike Capri's cliffs and soak in the beauty of its trails -- a great escape from the swarming crowds. Before setting out, stop at the tourist office, which has a map of the paths. One of the easiest treks is the short trail from Capri to Marina Piccola. From Via Roma in town, turn left onto Via Mulo; a series of steps and a dirt path will lead you down to the harbor through cultivated fields and gardens.
A more demanding hike is the Scala Fenicia (Fenician Staircase), which descends -- or climbs, for the most intrepid -- from Anacapri to Capri. Built by the Greeks in the 8th century B.C., it was the only access to the sea or to the village of Anacapri until 1877, when the current road was built. The steep path -- basically a long staircase with 881 steps -- rewards the daring with superb views. Another hike we recommend is the descent from Mount Solaro, on a clearly marked dirt path (after taking the chairlift to the top).
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.