I saw 1 or 2 Class C motorhomes when we drove through the tribal park, but I would never consider taking a Class A on those roads. I think the road to the visitor center is paved; but the roads on the scenic drive through the tribal park are all dirt, and they are rather uneven in places. Stay in Bluff, UT and take the toad to the tribal park. If you don't have a toad, there are Jeep tours through the tribal park you can take.
That being said, U.S. Highway 191 goes right through Monument Valley, and that is a good road. You can catch views of some of the formations, but the scenic drive through the tribal park is much better.
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