Been to the Southwest a few times. I get there by taking US 50 through southern Colorado. Visit the Black Canyon of the Gunnison briefly. At Montrose, go south on Colorado 550 (?) to Ouray. Truly charming town. Then through Durango/Silverton, beautiful drive. Self guided tour of Mesa Verde. West past 4 Corners to Monument Valley, US 160 to the Grand Canyon. You can come back through NM. I'm not that familiar with things in New Mexico. Went to Carlsbad Cavern, worth it for sure. I gave away my pot stash while sharing with a couple of guys. Didn't want to get nailed during my residency.
Went to White Sands; it's a lot of white sand. Meh. There are LOTS of Native American sites in NM. My brother and wife love Santa Fe for sure.
If you don't go to the Grand Canyon, then you're dead to me. It's a glorious site. Spend some time there; it takes a minute to appreciate the scope.