After making a splash in Palm Beach with boldface names, Mary Lou’s retro supper club comes to Montauk in early June; nibble on caviar and wagyu burgers between twirling around the dance floor. Summer residencies include New York’s Tusk Bar at sister spot Moby’s, and Caché Life’s monthly DJ parties at Sí Sí. The Surf Lodge kicks off its summer music series on Memorial Day weekend. 474 West Lake Drive, Montauk, N.Y., 11954. 341 Pantigo Road, East Hampton, N.Y., 11937. 295 Three Mile Harbor Hog Creek Road, East Hampton, N.Y., 11937. 183 Edgemere Street, Montauk, N.Y., 11954.