Many of the good places have been mentioned but make sure you go to Jerome, AZ. It's an old mining town. The volcano area near Flagstaff is Sunset Crater National Monument - it's amazing and make sure you drive far enough in the park to see the Painted Desert. Also, Meteor Crater near Winslow is interesting.
I know it's been mentioned but you must see Sedona - the red rocks are so impressive. It's one of my favorite places on earth.