Ventotene is not an island of wide sandy beaches, but it has plenty of lovely places for a swim. All along the coast, the reddish tufa meets the crystalline emerald sea to dramatic effect. The best way to explore the perimeter of Ventotene is by boat, but there are a few beaches you can reach on foot. The main spiaggia here is the dark sand Cala Nave, immediately south of the Porto Romano. In high season, it's horribly crowded here, but otherwise, this is a gorgeous spot -- a striking cove of striated tufa cliffs capped by lush Mediterranean vegetation. Cala Nave is equipped with a beach club, restaurant and bar, and kayak and pedal boat rentals. Nearby (between here and the port) is the swimming area known as La Peschiera, which consists of tufa platforms adjacent to the Roman fish tanks.
Beaches less convenient to reach by land are Cala Battaglia (on the southeast coast, a rocky beach accessible by a steep trail) and Punta Eolo (near the cemetery and Villa Giulia at the northern tip of Ventotene, it has smooth rocks for sunning and occasional nudists). You can also reach Parata Grande (on the west coast) via a tiring series of staircases built into the tufa amphitheater.
If you're able to go by sea around Ventotene, whether with your own boat or with a guided excursion, many more options exist for swimming (but expect rough surfaces underfoot). The best coves are along the southern half of the island, both along the west and east coasts.
South of Cala Battaglia is Parata Postina, an intimate black pebble beach with semi-submerged tufa arches. Farther along are Acqua Dolce and Le Saliere, largely deserted coves with coarse black rock formations but beautiful water. At the southernmost tip of Ventotene, the Piscine di Punta dell'Arco are natural swimming pools, carved by the elements in the black basalt rock. There's no comfortable place to lounge here, and you can easily burn your tootsies on the hot stone while getting into the pools, but the Piscine are a unique geological feature and very popular stop for boaters nonetheless.
About a third of the way up the eastern coast is Paratella, a tiny beach famous for the sheer black rock wall directly above it and the chromatic effect of the deep blue water below. The next major cove, about two-thirds of the way up the eastern coast, is Parata Grande. Especially enchanting at sunset, this is a narrow strip of sand and rocks backed by a high undulating wall of red tufa that sets geologists' hearts aflutter. Rounding Punta Mamma Bianca, you enter Cala Bosco, a delightful and deserted little cove with rocks and sand. It's best in the morning, as the sun leaves this north-facing spot rather early in the day.