Trata East, an outpost of an Upper East Side New York restaurant, likes to say that it brings the Greek Islands to the Hamptons. It uses sea salt from the Aegean, figs from Sparta, and fish that is flown here from the Mediterranean, which is then likely to be charcoal-grilled and daubed with lemon and capers before it is served. Wines and beer are exclusively Greek and ouzo is popular. There is a late-night lounge on Friday and Saturday, with a D.J. playing Mediterranean music, and a cafe menu.