Adventure cycling has two maps you may want to look at - Grand Canyon Connector and Utah Cliffs Loop. The cliffs loops has about 50% off road riding. Another map you may need is the atlas by DeLorme. You can make a nice loop through all the parks in southern Utah from St. George using paved roads. There are plenty of campgrounds so you shouldn't need to make reservations but they are always advisable if you are going to stay at a campground at a National Park. If you go off road be prepared to take several days worth of food and water some areas are pretty remote. One dirt road that is awesome is Hell's Backbone outside Boulder, Utah. Another neat road is the Burr Trail that goes from Boulder into Capital Reef National Park. You can then head south to Bullfrog and visit Glen Canyon Lake and the National Recreation area.
A large from St George could take you through Zion NP, Bryce Canyon NP, Capital Reef NP, Canyonlands NP, Arches NP as well as the Glenn Canyon National Rec Area and the Grand Staircase National Monument. The route I'm thinking about is about 1000 miles that is most road riding but about 25% is off road.