First I agree with everyone that Monument Valley should be on everyone's bucket list. If you enjoy westerns, then it should be at the top of your bucket list. (Yes I am a Duke fan).
Driving north from Monument you to come to a town called Mexican Hat, where you cross over the San Juan River. If your intent is to go to Capitol Reef National Park, there is a short cut called Utah highway 261 just north a couple miles from Mexican Hat, and it is about 35 miles long. You drive about 7-8 miles on good black top posted at 55 mph and the come to a cliff face. There is about 4 miles of twisting winding dirt road that will take you to the top (15-20 mph max). Then another 22 miles of good black top at 55 mph to US 95. This is the strangest highway I ever encountered (good black top, maintained dirt road up the face, and then good black top). There is no problem driving up the cliff face pulling a Camp Inn trailer, as I've met a fifth wheel coming from the other direction. This road is plowed in the winter time too, but I wouldn't want to be on fresh snow with a trailer coming down. I didn't see any 18 wheelers on Utah 261, so they obvious know about the quirky middle section.