Dinosaur Nat'l Monument at Vernal, Utah
Page, Arizona - slot canyon or boat tour; dam tour
Lake Havasu City, AZ area and one of the state parks
Prescott, AZ - Point of Rocks campground
Cottonwood, AZ - Cottonwood StatePark (near Sedona)
Grand Canyon - SOUTH RIM - if you can't get into one of their 3 campgrounds, try Williams, AZ (As stated, North Rim is not open yet so online it might show the sites are not available)
Flagstaff, AZ - some Indian ruins to tour and Meteor Crater - could stay at Munds Park just south of Flagstaff - lots of activities for kids