Utah's Highway 12, which runs through Grand Staircase-Escalante National Monument between Capitol Reef National Park and Bryce Canyon National Park, is perfect for a spectacular road trip almost any time of year, but especially in spring or fall. Highway 12 is the only road in Utah to receive the designation All American Road, and its scenery - with a combination of red, pink, coral and yellow sandstone formations, clear blue sky and blue-green desert vegetation - is truly amazing.
The "hog's back" near the town of Boulder, where the road drops off steeply into narrow canyons on both sides, is an unforgettable driving experience.
Along the way you can visit Kodachrome Basin State Park, Escalante Petrified Forest State Park and Anasazi State Park. Be sure to plan a stop at Calf Creek Falls, in my opinion the prettiest waterfall in Utah. Be aware that you must hike three miles each way, much of it through loose sand, to get to the falls and back. It's not terribly difficult, but you should be prepared with proper footware, water and a snack.