Three spots on the island offer great swimming. To get to Faraglione, walk 1km along the road west of town until you see a couple of rocks sticking out of the water just offshore. For something quieter and more remote, take the 4km cross-island trail to Capo Grosso on the far northern shore, where there is also a lighthouse.
Alternatively, take a right out of town and walk along the dirt road. The road forks 300m past the first bend; take the rocky path down towards the sea and keep going until you get to Cala Minnola, a small bay with crystal-clear water where, outside the month of August, you can swim in peace and tranquillity.
Levanzo's lone hotel, Albergo Paradiso, sits just above the port. A few people on the island also rent vacation homes.
Aside from the restaurant at the island's only hotel, Albergo Paradiso, there are a couple of bars in the port area serving sandwiches and drinks.