There is so much federal land out there, you can throw your tent up just about anywhere and be fine.
When I went, we spent the first night outside of Moab, two nights in the Needles District of Canyonlands NP, one night near Dark Canyon, and two nights in Capitol Reef NP.
Capitol Reef was really awesome! It is a little ways away from Moab, but was certainly worth the trip. Depending on when you get there, you may even get to pick some fruit from the trees of an old mormon village.
The outdoor activities are endless in the area. Before we went I used their tourist website (
http://www.discovermoab.com/) and got a ton of info and outdoor activities. We were only hiking so we didn't utilize any guides or services.
Definitely hit up the two national parks, Arches and Canyonlands. If I was a kid, I'd really enjoy floating the river or mountain biking in the area.
Pictures of the trip