Your post mentions camping in NYC but I'm guessing you actually mean in the general area. I don't know of anyplace you can actually camp within the confines of the city limits. That being said, you do have some easily available options. Just across the George Washington bridge you have access to the Palisades Park. You might want to go to your favorite search engine and enter that to see what there is. On the NY side of the Hudson River you have both Harriman State Park, just north of the city, Bear Mt. and eventually the Catskills. All of these areas have a tremendous number of options. If you won't have easy access to a car than Bear Mt. & Harriman will be your best bets because you can access them by public transportation. You will also find sections of the Appalachian Trail available via rail service near Pawling, NY.

Besides these options you might want to check out the NY-NJ Trail Conference. They offer trips throughout the year and it might be the easiest way to connect with folks who are already familiar with the trails in that area.

I hope that helps. Best of luck in finding what you're looking for. Take care and until next time...Be well.

snapper