+1 for many of the suggestions above! But it DOES depend on where you want to be....localize it more as Long Island is pretty large to drive all over!
If you are in the Bayshore area...............go to CAPTAIN BILL's.....the prices are a bit high.....but worth it!! Get the lobster!
More reasonably priced and on the North Shore in the Miller Place, Mount Sinai area is the restaurant portion of the seafood shop called LAND & SEA.....they have a lot of good take-out and buy to take home and cook....food!!! I personally love their "cocktail shrimp"!......their restaurant area isn't much to look at...but the food is great!