After two decades as a must-visit destination for club-happy kids, the Greek isle of Mykonos is recapturing the sophistication of its glory days, when Jackie O., plus entourage, regularly dropped anchor here for regular pit stops as they sailed around the world. Head to a local bar now and you’ll find a scene that’s a throwback to the 1960’s: multinational thirtysomethings in pressed linens clinking champagne flutes to a world-lounge sound track. Such is the scene at the island’s latest glamour spot, the David Rockwell and Colin Cowie–designed CBar (School of Fine Arts District; 30-2289/025-122; c-bar.com; drinks for two $50), at the Belvedere Hotel. Patrons flock to the indoor-outdoor space set in the hills high above the harbor, as much for the luxe snack menu (caviar finger sandwiches, anyone?) as for the staggering sunset and nighttime views across the town. Also at the hotel is Nobu outpost Matsuhisa Mykonos (30-2289/027-361; dinner for two $275), where the signature black cod with a miso glaze, and other Japanese-inflected dishes, are served late into the night. For a casual evening, visit the Astra Bar (Matoyiannis St.; 30-2289/024-767; astra.org.gr), in the center of the old town. This nightspot, popular with well-heeled weekending Athenians, has a ceiling with starlike lights and a candlelit outdoor patio wreathed in bougainvillea.