Chiefly popular with a party-loving crowd whose vacations tend to revolve around the latest see-and-be-seen beach clubs and discotheques, Mykonos has never been our favorite Greek island. We are most attracted to those that offer serenity, physical beauty and vestiges of Greece’s classical past. However, we recently discovered low-key cosmopolitan areas where one can keep the social scene at arm’s length. Besides its storied nightlife, Mykonos has much to recommend it: whitewashed houses, narrow marble streets, glamorous destinations and historic ones. An excellent day trip is to the sacred island of Delos, with its Doric temples, amphitheater, mosaics and Temple of the Lions, which was dedicated to Apollo in the seventh century B.C.