You probably don't think of New York City and camping as things that would go together. Neither did we.
Three years ago, when we were still planning the trip, one of us asked the other if they thought there were any RV parks close to New York City. A little Googling revealed a place called Liberty Harbor RV Park, which advertises itself as the "closest RV park to New York City". It's in Jersey City, and looks across the Hudson at Manhattan, which is a short 15-minute train- or ferry-ride away.