Go to Auto Club, get maps, travel guides and get on line. Here's some ideas=look them up and plan your trip! Most I have been to, others are on my wish list.

Mogollon Rim, Jerome (I don't think your trailer can do it-might have to leave it in a campground), Oak Creek Canyon & Sedona,

"Flag" : Montezuma's Castle, Walnut Canyon near Flag, Meteor Crater, Petrified Forest, Gallup (Forget Santa Fe=high priced tourist trap)

North Rim Grand Canyon, Mesquite Nev., Canyon de Chelly, Chaco Canyon, Wupatki Crater, Tuba City, Four Corners, try Sonoran Style Mexican food in Gallup/ABQ., Monument Valley

Colorado: Rocky Mtn National Park, Idaho City, Stanley Hotel (WATCH OUT FOR ELK!!),

Wyoming: Yellowstone (VERY CROWDED!), Buffalo Bill Heritage Center in Cody, Dinosaur dig in Thermopolis,(Road over Wind River Range vis Ten Sleeps is very beautiful), Chief Joseph Trail from Yellowstone (If camping, beware of grizzlies), Custer/Little Big Horn Monument.

I would recommend making this an exploratory trip to decide what you want to see on future trips! I grew up in the SW, now live in the PNW and can't wait to go visit friends on, near, or by the Rez!

Forgot: Mesa Verde (Again, steep, winding road not really suitable for trailers!()