Swimming & Sunning -- Although it's a summer resort, Capri doesn't have great sandy beaches because of its mountainous landscape. There are some spots for swimming, most of which have clubs called stabilimenti balneari, which you must pay to visit. Most people relax at their hotel swimming pools and take in the gorgeous views from there.
The coastline surrounding Capri is punctuated with jagged rocks that allow for very few sandy beaches. You can head for the Bagni Nettuno, Via Grotta Azzurra 46 (tel. 081-8371362), a short distance from the Blue Grotto in Anacapri. Surrounded by scenic cliff sides, with an undeniable drama, it charges 15€ ($20/£10). The price includes use of a cabana, towels, and deck chairs. Mid-March to mid-November, it's open daily 9am to sunset. From a point nearby, you can actually swim into the narrow, rocky entrance guarding the Blue Grotto, but this is advisable only after 5pm, when the boat services into the grotto have ended for the day, and only during relatively calm seas.
Another possibility for swimming is the Bagni di Tiberio, Via Palazzo a Mare (tel. 081-8370703), a sandy beach a short walk from the ruins of an ancient Roman villa. To reach it, you have to board a motorboat departing from Marina Grande for the 15-minute ride to the site. Passage costs 10€ ($13/£6.70) per person, unless you want to walk 30 minutes north from Marina Grande, through rocky landscapes with flowering plants and vineyards.
Closer to the island's south side is the Marina Piccola, a usually overcrowded stretch of sand extending between jagged lava rocks. You can rent a small motorboat here from the Bagni le Sirene (tel. 081-8370221) for around 65€ ($85/£44) for the first hour, and 12€ ($16/£8.05) for every hour after that. Prices can vary depending on the boat's size and the luxuries on board.