Made a similar trip with the wife a few years ago, drove from MS to California and back.
Cadillac ranch has already been mentioned a few times, I thought it was really cool. Sedona is one of the most beautiful places I've ever been, did the Devil's bridge hike there. Stayed in downtown flagstaff for a few nights, good food and brewery scene. White sands, Carlsbad caverns, and Saguaro national parks were all incredible. I asked when the bats would be flying out of the cave at Carlsbad, they looked at me like an idiot and said "April, they're in South America right now." So if you're expecting to see the bats fly out, don't.
Also ended up on hwy 82 in New Mexico, I thought to myself "no way this is the same hwy 82 that runs through Starkville" well, it is. Never in my years of living in Starkville did I know that if I got on 82 towards Winona and just kept going I'd end up going through a tunnel under a mountain in New Mexico. Anyway, enjoy your trip.