utah definitely has a lot of camping. we boondocked just outside of escalante, ut and that was close to the grand staircase, capital reef and dixie natl forest to the east and bryce canyon and zion to the west. thats about 400+ miles from denver (about 7-8 hr drive) and that would be double the distance for you...BUT since its your dad, i'd go with him getting the shorter distance.
you can then work your way northeast to moab and surrounding area and there are a lot of dirt roads and scenic views. there are pay campgrounds all over and quite a few state campgrounds usually around the parks like canyonland and arches. there is a good bit of BLM land scattered all over if you want to boondock. not sure when your going or what you want to do, but summer will be packed and hard to find places. we went in may/june and the entire state seemed packed. if you start low and work up, when its time to go home, it will be easy to hit I-70 west and then jump on 50 all the way to sacremento.
looks like you would take I-80 to reno and then 50 to utah and then 21 toward the escalante area. a fairly scenic drive getting there and then a straighter shot going home where you can hammer down..
hope it works out and you have a great time whatever yall decide..
