Another possibility is camping at Floyd Bennett Field (in Brooklyn on Jamaica Bay). Getting there with an RV would be a bit of an adventure for sure. Connections to public transportation are not bad, though; a bus that connects to subway stations goes by the park entrance (which is maybe a half mile from the campground).
The RV sites at Floyd Bennett are parking spots with picnic tables--there are no hookups, nor even a dump station from what I can tell.