Hi Paul @PGG

Not a backpacking destination, but Gateway NP has camping at Floyd Bennett Field, which is on Jamaica Bay, you can fish the bay, camp on the old airfield and still see the Empire State Building on a clear day.

Further afield, there are great hike/backpacking recommendations on the NYNJ Trail Conference site for hikes around Harriman State Park. Just remember that to camp at Harriman you need to stay at established shelter locations to limit impact on the terrain. Another option is Wawayanda State Park in NJ, which has some part of the AT going through.

Hope this helps.