If you are just wanting someplace to "hotel" while you are visiting the sites of NYC, then Liberty Harbor is your place. It is an easy ONE train ride into either the World Trade Center or 33rd St (Times Square) on the PATH train OR ride the water taxi that leaves the campground and go to Wall St.
There are lots of campgrounds OUTSIDE the area, but it takes at least an hour commute and changing trains, etc. LH is the most direct, but also is pricey. (It will save you $$ on commuting).
It is an easy, 2 1/2 block walk to the station, wait on a train, hop on, ride 10-12 minutes, get off and you are in the heart of NYC. The 33rd St. station is a hub for the subway, so from there, you can transfer to any of the burroughs.