The closest place to camp near Princeton is Washington Crossing State Park along the Delaware River in Titusville, NJ.
The Mountain Lakes Open Space Area, a “central park” in Princeton, consists of some 400 acres just north of the center of town, most of it open to the public. It has a wide variety of hiking trails- and two biking trails – some connecting to other trails outside of the area described here. Along with views of Tusculum, the estate built by John Witherspoon, and historic Coventry Farm, it features a great variety of open fields, several small streams and lakes, old stone walls, boulder fields, and old growth pine and hardwood forests. The area is divided into five sections: The Billy Johnson Mountain Lakes Preserve, including the Mountain Lakes House; Mountain Lakes North; John Witherspoon Woods; the Tusculum fields; and Community Park North. Most of the remainder of Tusculum, to the east, and Coventry Farm, to the west, is private open space.
Whenever mountain biking make sure that you are properly equipped including a helmet, water, extra tubes and repair kit, bike tools, etc. Also be aware of other people using the trail--hikers, folks on horesback, etc. By treating the land and others properly, we can all enjoy the trails.