Grand canyon (of course) but a short road south of Flagstaff to Sedona, AZ is definitely a must. A lot of beautiful parts especially in Utah, but Sedona, AZ is one of the best in the country. And take a big jug of water, a first aid kit, survival kit and camping toilet paper (not that you will need it, but if you do, genius!) State parks also have full bathrooms with showers. In New Mexico, great food, but if you don't have time a fast food option, "Blake's green chili/ cheese lot-o-burger" is one of my favorites.
Santa Fe is nice, but might be a bit out of the way and unless you are really into art galleries not sure it will be worth it for you. I never was too much of a fan of Albuquerque, but again, try some mom and pop restaurants and I bet you'll find something good.
If you do stop by Vegas and eat at the China Poblano restaurant inside the Cosmopolitan, please tip well, my daughter works there.