pjcnlv, thanks for the link. We're planning to head back to UT this Spring (hopefully before it gets too hot).
I would suggest two base camps for route 12 & 24. Either Ruby's or the KOA at Cannonville for the area of Bryce Canyon, Kodachrome State Park, Red Canyon and possibly for a day trip to Zion. After that, drive route 12 to Torrey. We have used Thousand Lakes RV Park there. Capital Reef NP is near Torrey and the drive on route 24 to Hanksville is easy and scenic. If you want to move on to Moab for Arches, Canyonlands and Dead Horse Point State park, you will pass Goblin Valley State Park on the way up to I70. Lots of parks for your size rig in Moab. Assuming you have a car in the enclosed trailer (which you are going to need), drive route 128 along the Colorado River at least as far as Fischer Towers for some great scenery.