Do expect to pay higher than average prices for camping, at least along the stretch I did. To give you a frame of reference, the two state park campgrounds on the route in NJ (Bull's Island and Worthington State Forest, both not open until April 1) charged $20/night this year. Commercial campgrounds will almost certainly be higher unless someone is feeling generous or sympathetic to your cause, which is something I never encountered. I paid $30 at one place in CT, and that was in '99. The place did have a bar, a pool and a hot tub, but come on. I also paid $28 in Goddefroy, NY just north of of Port Jervis, NY, and it was "off-season." This year, that place charged $36/night. $38 if you wanted a site next to the river.
The main route does not pass close to NYC. You would have to take the spur from Lambertville, where the route crosses into PA, to somewhere in north Jersey (Summit, I believe) and then hop the train. The stretch in NJ (crossing back into PA for a time) and on up through the Delaware Water Gap on the NY side is, for the most part, quite pleasant.