We just got back from there:
Our favorite in the area is Dead Horse Point State Park, but it is very difficult to get reservations.
On the recommendation of a friend, we just stayed at Portal RV Resort for 2 nights, which was very nice and $$$, but without much character. We like to interact with other campers, but here most of the guests were older (we're old) and stayed in their RV's with the AC running. I was the only one in their pool.
We visited Archview RV Park, which seemed more interesting, and it would have suited our needs better.
We stayed next to Slickrock RV Park, which also looked nice, and was more active.
Many years ago, we stayed at Moab Valley RV Park, and would probably stay here on our next visit.