La Sirena is a restaurant and hotel that sits right on the water in Pecorini a Mare, the island’s tiny pebble-shored fishing village. More than a restaurant, it is Filicudi’s living room. After dinner, people naturally gather in the little harbor square outside. The food is classic Sicilian: grilled catch of the day, raw fish, and the renowned La Svergognata cake—a sponge layered with ricotta, dark chocolate, and wild-fig preserves.