I like to ride out to Cold Spring, NY, on the other side of the Hudson, and wild camp out there. It's about 68 miles from midtown one way. Here is a map of a trip I did last summer:

http://www.gmap-pedometer.com/?r=4029405

The final spot in Cold Spring may not be exact, sorry. But when you are riding south along Route in Cold Spring, you eventually reach a trail entrance where some cars can park. I think it's part of the appalachian trail. It's easy to find a nice spot in the woods for the night.

The second day I rode out to New Paltz and camped at an actual campsite out there, and the day after I rode to Clinton Corners to meet my GF. You could always take metro north for an hour out of the city and start somewhere farther north on the hudson.