East Hampton Deli's/Sandwich shops
Easily the best deli in the area is Luigi's, in Amagansett, and Pumpernickel's (which is next door) is good as well. Both are basically across the street from Goldberg's which was also mentioned in here (and is probably the best bagel place/NY style deli in the area).
Another great sandwich place is Breadzilla, which is in the Wainscott area near Twice Upon A Bagel. The Seafood Shop, which is also in that area, also has sandwiches and good lunch fare.
Finally, for kind of a hidden sandwich gem, try Cavaniola's Gourmet in Sag Harbor. They don't have a lot of sandwiches to choose from, but all of them are truly excellent.
Goldberg's in East Hampton is an old fashioned NYC deli. Or were you looking for something more unusual? The Golden Pear chain is very popular. Most delis in the Hamptons are aimed at the contractors and working men. Did you want something more upscale, or just a hearty meal?