Ponza is an island destination mostly frequented by Italians (especially Romans and Neapolitans, as it's just a hop, skip, and a jump away by boat) that is largely undiscovered by foreign tourists.
A must-do in Ponza: rent a motorboat on your own, or take one of the guided boat tours (spaghetti lunch included!), and visit the beaches that aren't reachable by foot, and the nearby islands. Palmarola is a tiny island near the north end of Ponza (it'll probably take you 20 minutes to cross there from Ponza) and almost completely uninhabited. Palmarola's beach is only frequented by other boaters and tour boats and offers a French-style restaurant. Instead of sand, the beach is formed from small pebbles. The water is absolutely crystal clear and as calm as a swimming pool. This is a good spot for snorkeling, so bring your mask and flippers.