By all means, go see the Grand Canyon and then Mt. Rushmore, Yellowstone, the Tetons and maybe the Wind Caves. Then if you have time on your way home, drop down to the bottom of Utah.
In lower Utah, do Arches NP, Natural Bridges NM, Zion NP, Bryce NP Canyon Moab (and not you don't need a built up Jeep to see all of it) and Canyonland NP. After seeing the Grand Canyon, which you can only really see from the top looking down unless you're a very serious hiker, we enjoyed the southern Utah areas much more.
In the Canyonland area there is much more to see. You can look down on all of it from the top, then you can drive down into the canyon and look up from the bottom. You won't be able to go down in the canyon with the Class C, but there are lot's of places that rent Jeeps for the day. From the 1940s & 50s there was a lot of mining down in the canyons which required access. So there's lot of dirt roads / trails that the BLM maintains for people to use. When I say maintain, they keep them in a somewhat passible condition after rainstorms. Anything with somewhat of a decent ground clearance can access a lot of them.
While I'm glad we did the Grand Canyon, I'm glad we did it first so that we weren't disappointed. There's just so much more to do and see in southern Utah.
Bill
