This fine walk can be done as a circuit from the centre of Capri Town. It's spectacular even by Capri standards, taking in a necklace of west coast sights including the Arco Naturale, Faraglioni and several grottos and belvederes (lookouts). Most of the path is paved and there are quite a few steps, though it is not inordinately difficult. The walk should take about an hour and is roughly marked on most local maps available at the tourist office.
Head east out of Capri Town to the Arco Naturale, a curious eroded-limestone arch dating back to the Paleolithic era and formed by millennia of natural wear and tear. At the end of Via Matermània, backtrack to Le Grottelle restaurant and take the set of stairs beside it (Passeggiata del Pizzolungo). About halfway down you’ll pass the Grotta di Matermània, a giant natural cave used by the Romans as a nymphaeum (shrine to the water nymph). You can still see traces of the mosaic wall decorated with shells. At the bottom, continue down the path as it follows the rocky coastline south. The striking flat-roofed red villa you eventually see on your left, on the Punta Massullo promontory, is Villa Malaparte, the former holiday home of Tuscan writer Curzio Malaparte (1898–1957). Carrying on, the sea views become increasingly impressive as the path continues westward around the lower wooded slopes of Monte Tuoro. A few hundred metres further along and you will arrive at a staircase on your right, which leads up to the Belvedere di Tragara, a prime viewing point for the pointed Isole Faraglioni. From here, follow Via Tragara back to the town centre.