Concierge.com's insider take:
The sacred isle—20 minutes by taxi boat from Mykonos—birthplace of Artemis and Apollo, is an essential day trip (you can't stay over). One of the world's largest archaeological sites, it contains some phenomenal structures, including the Agora of the Competialists, a theater with stunningly detailed floor mosaics, and temples dedicated to various deities and religions (Apollo, Isis, Dionysus, Syrian gods, even a synagogue) that attest to the city's cosmopolitan nature. There's a small museum with some terrific artifacts, and a climb to the highest hill is essential, if only for the views of the Aegean. Arrive as early as you can and bring water and a hat; it's hot and crowded, and the last boats leave around 3 pm.