If you can time it as a late lunch/early dinner, you can take a cab into Jackson Heights for some Indian food or Flushing for Korean. I particularly like Kum Gang San in Flushing.

The Queens Museum of Art has a very cool panorma of New York City--a detailed scale model that you walk around. It's huge and just really neat to see.

If you want to cab it into Astoria and it's a nice day, visit the Bohemian Hall and Beer Garden for some food & drink. Bring a book and you can hang out in the garden (picnic tables) for a couple of hours and then head back. Otherwise, you can go to the Museum of the Moving Image, also in Astoria. Astoria is much closer to LGA than JFK but if you don't mind spending the cab fare it's a fun neighborhood.