The problem is that schleping around Manhattan with a roller board is going to get old real quick. If the OP wanted do some sightseeing/shopping/lunch I would recommend taking the bus to Jackson Heights with lots of places to shop and eat along the main drag. And then take the E train out to JFK. But again walking around with bags will become quite annoying, particularly if the OP hits a hot summer day.

OP, there is not a lot to do at Terminal 8 (AA) at JFK. There is a somewhat decent bookstore in the first concourse. If you don't have AC access, you can purchase a day pass for $50. This will allow you to shower before your International flight. Also, since you are flying International you might get an AC Angel to give you a couple of drink chits. My suggestion is to shower and change into new clothing, get a good book and some music, and have a couple of drinks in the AC along with a nice lunch. Possibly even a little snooze although both of the ACs at JFK tend to get noisy towards late afternoon and early evening.