I live in Rockville Centre L.I. and I have my personal favorites for plane spotting:
I have a handheld scanner, so Before going anywhere, I listen and only if runways 31L and 31R are in use it's worth of going to Kennedy Airport.
The best spot when they are landing on runway 31R (Which is the usual, not the 31L as JZ said), is COSTCO, you can get there by Peninsula Blvrd, or Rockaway Blvd.
If planes are landing on runways 22s, the best place is a little driveway in the middle of Rockaway Blvd, I tried it once, and nobody said nothing, but I think the other cars there were Feds, so I prefer COSTCO.
In La guardia the absolute best place is the College of aeronautics, which has a small tower for spotting. You can go there and say you are going to find some info about the college, and they let you in, then you take the elevator to 3rd floor and you are there, everithing from cameras, scanners and telescopes are allowed.