For restaurants - I would suggest skipping the Manhattan trip and staying in Queens. Right near the Jackson Heights station mentioned above are some of the best Indian/Thai /Vietnamese restaurants you could eat in - better than in Manhattan.
Check the http://www.chowhound.com/boards/outer/outer.html
message boards for recommendations on restaurants such as Jackson Diner or Sripaphai, among others. Then after a good lunch, go directly from Jackson Heights to JFK.

If you want to stop at a museum, go to the MOMA QNS, right next to the 7 train.