Travelling in the area of NYC

Dear experienced travelers :)

In the middle July I'm going to stay the first couple of days within NYC but then I will have about 6 or 7 days which I don't want to spend in the city. My return flight leaves from JFK.

Maybe that you could give me some advice what I could do/visit during these days? I would prefer things that could be done outdoors, I'm quite sportive - so hiking, biking, swimming etc. would also be an option. I would not prefer visiting other cities - it should be quite a contrast to NYC though ;)

I would really be grateful for any hints that you may have.

Thanks in advance!