Where is there real wilderness camping outside of New York City?

The closest place for REAL wilderness camping would be six or seven hours away (depending on the specific location chosen) in the Adirondack Park. It's over six million acres and includes a 2.3 million acre forest preserve which the NY State Constitution mandates must be "forever wild." That preserve is the only public land in New York in which you can camp anywhere you want to (except, during the summer, anywhere over 6,000 feet elevation, because of fire risk) without having to be in an actual campground -- though there is that option, there are dozens of campgrounds that vary greatly in the level of amenities that are available and how crowded the sites are.

Wikipedia has a pretty good writeup about the park:
http://en.wikipedia.org/wiki/Adirondack_Mountains

One campground that is worth considering, and is one of my favorites, is called Indian Lake Islands. The appeal, if you can get one reserved, is that there are campsites on islands that can be reached only by boat. Some islands have as few as one or two sites, so privacy is better than most organized campgrounds. The whole area is heavily forested, so even if there are other sites around it's not like that "large lawn" feeling. Info on the facility is here:
http://www.dec.ny.gov/outdoor/24471.html

I also like Eighth Lake (apparently at some point they ran out of names for the many lakes, and just started using numbers!):
http://www.dec.ny.gov/outdoor/24465.html

There are some reasonably similar campgrounds in the Catskills, but generally it's more crowded there and you don't have the freedom to just pitch a tent (or use an available public lean-to at no charge) like you would in the Adirondacks. The upside there is it's less than three hours away from NYC.

Long Island.