I think it's a good idea too. And unlike others on this thread, who never have a good thing to say about New York or New Yorkers, I have actually been to Floyd Bennett Field. Currently, you have to buy a 'Special Use Permit' to get into the park. Annual fishing parking permits cost $50 and they'll inspect your equipment before issuing one. I'd use mine to gain access to Floyd Bennet Field and Fort Tilden, on the other side of the bridge on the Rockaway peninsula. That's a cool place too with old naval batteries, a maritime forest, and a deserted beach. The park police stable their horses there too.
The fortifications protected the entrance to New York Harbor during World War I and World War II. Their 16-inch guns could fire a shell 30 miles out to sea. During the Cold War, Fort Tilden became a Nike Missile installation. 
My dog was once chasing a rabbit across the top of one of these when it just ended. She didn't realize it stopped . . . she didn't. I wish I had caught on film that WTF look on her face when she was flying through the air.
It's a trek into Manhattan from either Floyd Bennet Field or Fort Tilden: the Q35 bus to the end of the line and then a subway . . . a good 90-minute trip with the right connections. But it gives the visitor a taste of the vastness of New York City they'd otherwise miss. Too many visitors never set foot outside Manhattan; it's their loss.
I like the idea of the campground because there are no hotels in the Rockaways and it would give me an inexpensive base when I'm visiting.