Black-tie is required for Le Bilboquet Sag Harbor’s New Year’s Eve dinner with two seatings. Gurney’s Montauk always does it up for New Year’s Eve. Choose from two seatings at Scarpetta Beach with entirely different menus. The later one with more decadent dishes also adds a fifth course and champagne toast. Tutto il Giorno’s Southampton and Sag Harbor restaurants will be serving New Year’s Eve dinner. 1 Long Wharf, Sag Harbor, N.Y., 11963. 290 Old Montauk Highway, Montauk, N.Y., 11954. 56 Nugent Street, Southampton, N.Y., 11968; 16 Main Street, Sag Harbor, N.Y., 11963.