Flying in NYC
I live in the area and think the idea of getting a car and driving around is a good one. If you don't have regular access to a car White Plains is close to the Metro North and I think you can take a bus to Caldwell from the PATH. Morristown might also work, you'd need to get a taxi from the train station.
I would stay away from Teteboro as you can get long ground delays.
Depending how long you are in the area there are a few flying clubs you can join. Also AOPA list seminars etc which can be a good way to get in touch with local pilots.
20driver