We stayed at the NPS Morefield CG in 2011 in our van RV. Bear in mind it is a long way from Morefield to the park's sites. It is not like Zion. There's no shuttle, free or otherwise, running from the campground further into the actual cliff dwellings etc in the park.
There are very few camp sites with electric hookups and all the facilities are dated. There were tours (we took one in a minivan and enjoyed it a lot) that picked up at the campground office/grocery store/showers area, a bit of a hike from our site.
We also stayed a couple of nights in Cortez. I think that's the way to go, with a rental car.