The traditional tension between the establishment and the newcomers is resolved at the Montauk Yacht Club, a nearly century-old yacht club favored by the Gilded Age dynasties that’s now been updated for the luxury-boutique era by the proprietors of a couple of other successful Montauk properties. The Lake Montauk setting feels splendidly private, and the rooms, though luxe, are unpretentiously clad in whitewashed timber. And the facilities are comprehensive: two pools, a beach club, a marina, as well as fitness classes, tennis lessons, and a pair of restaurants, a wood-fired pizzeria and a seafood-focused fine-dining venue.