NYC Aviation is the source of info.
http://nycaviation.com/new-york-area-spotting-guides/
Used to live in NYC and spotted with the NYC Aviation crew.
May will be nice spotting weather. If you're going to go out on a weekend, check the forums to see who else will be about. Perhaps even get some contacts.
For JFK you don't necessarily need a car. You can get to most locations by train and bus. If they switch runways a car is helpful, but again, you can use public transport. I spotted at JFK over a dozen times with no car.
Let me know if you have any questions.