On our 2010 odyssey once around the perimeter of the U.S. we were also faced with the problem of finding a campground close to NYC.
The first place we found was Blydenburgh County Park on Long Island (
http://bit.ly/17eIdJG). What a great find. This is a huge park with a lake and large dog run. In the middle of Long Island it's like an oasis. When we were there in late June of 2010 there were only seven out of 50 campsites being used. We had an entire corner of the campground to ourselves.
Now the bad news about this campground, although it is gorgeous, you won't have any electrical hook-ups. We had a generator which we ran during daylight hours when we in camp to drive the ac unit. And the second thing is that many of the roads/highways on Long Island only have clearance for 6˝ foot vehicles. So although our older (non-RV GPS) was telling us to turn, we had to make sure we'd be on a road with enough clearance. We got it figured out, but not after our unit informing us over and over again, "Recalculating".
We also discovered that we were the only RV on any of the Long Island roads the entire time we were there. We didn't see one other unit, not even a Class B.
But I'd go back there in a heartbeat because you don't even know you're within the hustle and bustle of suburban New York when you're camping here.
The other place we camped is the KOA 40 miles north of NYC in Newburgh (actually in Plattekill (
http://bit.ly/17eKHro). This too is a gorgeous campground, but with all the amenities. They offer daily bus trips into the city, so you can leave your vehicle at home. Parking a 3/4 ton pick-up in the city is a hassle, since parking garages not only charge an arm and a leg many have only a six foot height limit. And to that the turning radius of our trucks and I'd not recommend driving in the City.
The area around Plattekill is beautiful. The Hudson River valley has more than its share of history, including FDR's Hyde Park.