I spent a couple days there camping off of Hwy 191. I went east off of the highway on Willow Springs road (I think) and found a lot of areas to camp there. The further east you go, the less likely you are to camp next to someone. And there's some good exploring out that way, and it leads to the back way in to Arches (no pay!).
Also, south of town, west of the highway there's copious areas to put down a stake. Arrive early and check things out.
So much to see, so much to do.