Try Linden, New Jersey (KLDJ). I believe it is one of the closest GA airports to NYC (or, at least it's one of the closest in NJ).
Also in NJ, you could look at Morristown Muni (KMMU), Essex County (KCDW), or perhaps Central Jersey Regional (no ICAO identifier, only FAA identifier 47N).
There are several other airports in Northern NJ. One or more may suit your needs.
Have you looked at
www.airnav.com?