OP,the roller board and backpack are going to make walking around Manhattan a real pain. So if you do come into Manhattan, I would choice one place-Central Park/Bryant Park, etc. No there is not much around the airports.

My suggestion is tell us your interest (art, parks/open space, food/dining) and we can direct you to those destination. Also, if you let us know what terminal you are going out of at JFK we can give advise on what those terminals may have to offer. Personally, with bags I would just head to JFK and camp out.