As 2gypsies said much of the good boondocking close to Moab/Canyonlands has been shut down due to overuse/abuse and I strongly suspect lobbying from campgrounds. There is some out Kane Creek road along with some first come primitive camps near the river a bit closer to town along the same road. All the good stuff south of town has been shut down, not sure about up north.
We like Horsethief campground on the way out to Dead Horse Point for more "away from it" camping, if visiting Moab proper Ken's lake has some nice sites, early/mid May is prime time so I'd arrive mid week and look for a spot.
The link 2gypsies gave you is the same one I was going to post. Good luck and have fun.
'99 Alpine 36SDS/8.3 ISC 330 Cummins
Or
'05 Lance 845
'06 Super duty SC/SB 6.0
Upgrades include: StabilLoads, Air Bags & Timbrens,Swaybars
Usually towing an '01 Wrangler, lifted/locked on 35"s or a mildly built '98 Cherokee on 33"s (only one locker)