The entire historic center of Patmos is a UNESCO-protected settlement, so very few restaurants and bars are granted a license. In a beautiful stone house built in 1673, Astivi is the oldest bar in town, and Patmos aficionados wouldn’t dream of going anywhere else. Every night, they congregate on the flagstone terrace draped in bougainvillea to gossip over watermelon daiquiris. The Mediterranean-Asian cuisine (veal carpaccio with pickled artichokes and Parmesan custard; lobster orzo with tomato, ginger, and marjoram) is good, too. Unlike most bars in Greece, Astivi operates with strict hours: It closes at 2 a.m., when the monks from the neighboring monastery of St. John wake for morning prayers.