You will almost certainly be departing JFK terminal 8 and that terminal has a 24 hour Au Bon Pain past the entrance to the AC and across from the area for Caribbean check-in. Might not be a bad idea to see if they have an item or two to take along just in case you don't like the Y fare to LHR plus it's your last chance to pick up take out items at NY's relatively bargain prices if you are staying in London and not connecting. ;-)

And remember your flight is one of the few on which AA serves a complimentary meal in Y and allows special meal requests. I always ordered a special meal and got something marginally better than the standard fare. Consider that if you are flying back to the US on AA.