As others have said, Liberty Harbor is your best bet overall for seeing the city. There are a couple of other options that might work, but would be less convenient.
Croton Point Park (a county park)--full hookups available, and commuter rail to Grand Central is right next to the park. I've heard pretty good things about it. You will spend more time getting to the city from there than from Liberty Harbor for sure.
Floyd Bennet Field, in Brooklyn on Jamaica Bay, is part of the Gateway National Recreation Area and has camping available. The RV sites are just marked-off areas around the edge of a very large concrete expanse (a former seaplane station) with picnic tables and nothing else. There's a city bus that runs to the entrance of the field, a good little hike from the camping area, and thence to the subway. Getting to Floyd Bennet Field with an RV is interesting. From the north, at least, probably the best way is to go over the Tri-borough bridge and follow I-278 (aka the Brooklyn-Queens Expressway) to Flatbush Avenue and follow that all the way across Brooklyn. The more obvious routes involve parkways that RVs can't use.