I'm surprised Tamburino's hasn't been posted yet. Definitely one of the best values to be had on Long Island, it's a small, very Italian deli that has remained a well kept secret in the area.
The Tamburino's trademark is that it makes the hugest sandwiches you'll ever see, no exaggeration. It's a favorite with locals who manage to work up an appetite for lunch. For those of us who take human-sized bites, one sandwich is enough to feed two. This explains why the line at lunchtime is usually out the door. Try the "Tambi's Special," an Italian cold cut hero with vinaigrette dressing.
Tambi's is in Cedarhurst in western Nassau near the Queens border on the south shore of Long Island. They are on Washington Ave, not far from Peninsula Blvd and Rockaway Tpke, and they deliver to JFK (or at least they used to).