I, too, escaped Long Island late in my youth. I now get to go back periodically for work, and get to stay long enough to get my food fix before I need to head back home.
The places to eat on Long Island sometimes fall more into categories than actual names of restaurants. For instance, I think that one of Long Island's greatest food contributions is the delicatessen. This is not delicatessen like Katz's or Carnegie in NYC, but rather something you would find in most any strip mall. Many are of similar good quality, but you will find favorites based on what you like to eat, and what any given deli's specials might be. The key is to sample a few. Why delis? Well, most every one serves Boar's Head meats. Here in Florida, you are most likely to find BH only in Publix. Long Island -- virtually anywhere. Also, the deli is also the morning pit stop. Most places will serve a breakfast special consisting of a couple of eggs (your way) on a hard roll with/without bacon, cheese, etc., plus OJ, coffee, and potatoes for about three bucks. I usually don't know delis by name -- I just know which locations I like best -- other than that, they can often all look the same.
I also feel the same way about diners. You are more likely to find a good diner, with a notable special than you would be to find a bad diner with nothing of note. Diners are also an excellent source for the sit-down breakfast.
Along the same lines, if you are a fan of Italian, and particularly, thin-crust pizza, you will also find jewels in most any strip mall up and down the Island. I was in town with some colleagues who wanted to go out for Italian -- and their idea was Macaroni Grill. I shuddered. I told them we could go to a place that would be much better, and we could walk from the hotel. Sure enough, I had never even been to the place, but they all agreed it was the best Italian they'd ever had. I have frequented the place often, ever since -- Conca D'Oro's on Commack Rd -- just off the expressway (Exit 52, I think, heading east).
Another of my favorites on Long Island is a somewhat underrepresented group here on Roadfood.com -- chinese. There is a place named Hoi Ming on Montauk Highway in West Sayville (just over the Oakdale border -- kind of across from St. John's University). It is a stand-alone restaurant, which has been at the same location, under the same ownership for about 25 years now -- quite long for this genre. You will often find a wait for dinner -- most definitely on the weekends. Arguably the best egg roll I have ever eaten. The last time I was there, I ordered a half dozen to fly home with me. Also, if you are a more adventuresome eater, do yourself a favor and order the beef and broccoli somewhere else, and get something a little more exotic here. Their spicy stuff packs a little bit of a punch, if you like such.
Lastly, if you like brew pubs, you will find a hidden gem out in Patchogue, on Main Street -- not far from where the old Sweezey's used to be. Brickhouse Brewery makes a fine pint of beer, and the food is quite tasty, too. I think they might have live music on Friday nights, too. They usually offer a price fix menu for around $15-18 that includes app, entree, and desert. Not too unreasonable.
Hope this helps some. I am sure I will think of some more -- I am just bad with names -- I just know where to go!