The culinary bar has been raised so high in the East End that local burger joints compete with gourmet shops. That is, if you know where to go. In Sag Harbor, Bay Burger owners Joe and Liza Tremblay bake their own buns and grind their own beef. They even make their own ice cream, in flavors like Cookie Jar, Mud Pie, and Black Cherry. Each pint comes with the perfect tag line: "It's from the Hamptons, so you know it's rich."