There's some great dispersed camping, just east of and above, Natural Bridges National Monument. Just drive up County Rd 228 (A.K.A. FS Rd 88 on the Nat Geo topo/ A.K.A. Elm Mtn Rd on google maps) off of the 275, shortly after it starts off the 95. There's plenty of dispersed camping at the top of the bluff with awesome views of Natural Bridges and the entire valley. Just take a left or a right at the top of the plateau (after the sharp bend in the road). Collecting dead wood for campfires is allowed.
If you decide to take this trip, Hwy 261 through Muley Point is a worthwhile route, giving you an awesome view of the San Juan River and Monument Valley from a 1,200' sheer cliff.
The hiking in the park is amazing. There's hundreds of Ancestral Puebloan ruins throughout the canyons, most are unmarked. A compass & topo wouldn't hurt as even the park's 8.6 mi loop trail is not marked once you are down in the canyon. Arch Canyon, just east of the park, is also definitely worth checking out. It has more Ancestral Puebloan ruins and quite a few large arches.
If you can, try to time the trip when there's no moon--the park is the first designated International Dark Sky Park. They have a free astronomy program with a huge telescope on weekends.
Here's a map showing where to start looking for dispersed camping:http://maps.google.com/maps/ms?oe=utf-8&client=firefox-a&ie=UTF8&fb=1&gl=us&hq=Canyonlands+National+Park&hnear=Canyonlands+National+Park&hl=en&view=map&ved=0CBgQpQY&ei=x8q0S57UAYSGiAOoxMVT&t=h&msa=0&msid=112824717363844462766.000483305adb35c5bcc2f&ll=37.600972,-109.955807&spn=0.051273,0.111151&z=14