Lunch spot between JFK and Kingston
In Kingston, about a mile west on Rt 28 from the traffic circle is the Hickory Barbecue and Smokehouse. It can be a 2 hour ride from JFK, so you will really be hungry.
If you want something sooner, there is a Ben's Deli in Bay Terrace, right near the Queens side of the Throggs Neck Bridge. Ben's is the old Kosher type deli with excellent pastrami, corned beef, etc. Unfortunately, I cannot think of too much in between.
Since you are flying into JFK you might also want to consider eating in Queens. It is the most ethnically diverse urban area in the world and your ethnic food choices would be considerable. The Outer Boroughs Board is a great starting point if you are interested.
I assume that your route is taking the Van Wyck Expwy to the Grand Central Pkwy to the TriBoro Bridge (which leads to the Major Deegan Expwy in the bronx; the Major Deegan turns into the NYS Thruway. in that case, following the suggestion of EM23 for thnic food in Queens, Sripraphai (in Woodside,)is not too far from your route and widely considered among the best Thai food in the NYC metro area. A bit further north, not too far from the Airmont Road Thruway exit is Sutter's Mill along rt. 59, to which I have not been but which has received positive mention at this site. And if you can tolerate your hunger for a bit longer, get off the Thruway at Exit 18 (Newburgh) and take Rt. 9W north to Kingston. along the way, stop in Marlboro at the Raccoon Saloon for one of the best burgers (and homemade potato chips) in the Hudson Valley.