Yes, I made a reservation back in February and I think I got the last campsite. The cost was $40 per night and there was only electrical at the site. No water or sewer. The campsites were paved and had a very nice shade structure with picnic table, a tent pad, and a fire pit and the sites were nicely spread out. There were also vault toilets. There wasn't water available anywhere, but they had a dump station with non-potable water. This campground was probably one of the cleanest I have ever been too. Personally, I think $40 was a little pricey, but it's in a beautiful area and there are some wonderful hiking and biking trails in Dead Horse Point State Park.
There are many dry campsites and BLM land all over the area. I think the dry campgrounds were $20 a night and first come, first serve. We spoke to a couple staying in one of the dry campgrounds and they liked that there were mountain bike trails right outside their door. There was also a lot of mud because of the storms.
We checked out one called Horsethief Campground off of Hwy 313 and it was really nice with a ton of sites. The sites were big with lots of space and they had tent pads, a picnic table, and a fire pit. Also there were vault toilets. I think when we go back we will probably stay there because it was in a really pretty area.
We drove into the city of Moab and there were 3 or 4 RV parks in town. They looked like typical RV parks with full hook-ups. I spoke to another couple staying in one of these and they liked the RV park in town because they could walk to all the shops and restaurants.