We were there a number of years ago without an RV but remember signs offering dry camping on the road to the Visitor Center or in the vicinity. Can't find any references on the common review sites. Ha...
You can camp in the Valley of the Gods, Gooseneck State Park, and I think I heard near Mexican Hat. I did not see anything on the Navajo land at Monument Valley and frankly would be surprised if they did allow it. It would go against their commercial interests.