Driving JFK-East Hampton
If you are coming from JFK -- you might want to go through Long Beach to the Meadowbrook to Ocean Parkway (you can pick this up through Jones Beach) and the turnabout. Take Ocean Parkway to Robert Moses parkway to Rt. 27and then to East Hampton.
On the way, you have Lido Deli, Long Beach Diner on Park Ave
If you are driving from JFK to E Hampton you will probably want to stay on the south shore (Southern State Pkwy, Route 27) and avoid 495.
Cedarhurst and Five Towns area are near the back door of the airport (Rockaway Blvd/Tpk) and have a lot of kosher places. King David deli restaurant has gotten good review here. If you are really looking for this type of food you might want to ask on Kosher board. If your trip is on Friday a lot of these places may close early afternoon.
As someone else said, there is no paucity of Greek diners on LI. There are plenty to choose from along Sunrise Highway (route 27). Two that get favorable mention are the Peter Pan in Bay Shore and the California near Patchogue. I like the Terrace diner in North Babylon. All of these are along Sunrise Hwy.
Downtown Patchogue also has several Colombian restaurants with good rotisserie chicken etc and a BBQ place on West Main St. This should be about a mid-point on your trip to East Hampton.
I would go to South Bay Diner, Sunrise Hway Lindenhurst, over Peter Pan and California. Much more extensive menu, and the quality is a bit better. California always seems to have a musty smell in the main dining area.
Princess Diner is a classic, if you can wait until you get to Southampton.
If you want to stop in the Hamptons, Goldberg's Deli in Easthampton is considered very authentic (the owner owns several in the NYC area). Located behind Wei Fun and Turtle Crossing, off the main road.
Diners: Hampton Diner in Hampton Bays (get off Sunrise at Rte 24 South it's right there) or Princess Diner in Southampton where you make the sharp left turn to go east.
Both are large, authenic NY diners with good food. Both open 24 hours as all diners should be!
There is a great "deli" called Kitchen Kabaret on Glen Cove Road (East Hills) off the Long Island Expressway, around Exit 41 or 42. Make a left onto Glen Cove Road NORTH and it will be on the left hand side about 1/4 mile on the left in a shopping center near a CVS and Exxon/Mobil. It's not only a deli, but it also has great italian (pizza, garlic knots, panini, etc), desserts & bakery, sushi, smoothies, salads, soups, fajitas, a TON of amazing salads and hot food... as well as the biggest selection of sandwiches you'll ever see! Robert DeNiro and crew used to stop there while filming Meet the Parents AND The Good Shepherd.
There's also a really really good pizza/italian place (rated best on LI) in Holbrook off the LIE, around exit 50 something... called Mama Lombardis.
There is a diner on every corner in LI, I think most are pretty good due to the prominent Greek population on LI.