The link below has good info on Moab trails.
Latitude 40 makes great trail maps. It's too late to buy them on-line, but you can also find them at many shops in Moab.
For an unplated bike, I would say the best campground is Archview about 10 miles of town. There are trails around it that head in almost any direction. All other campgrounds require riding at least some paved roads to get to the trails.
Small world. A few of us will be towing our bikes from Ohio to stay next week at Archview. Maybe we'll see you there.