I've been across to Flagstaff (enroute to Phoenix) during Spring Break, found the weather OK across Texas, New Mexico and Arizona on I-40.
But this is about the time of season change, it can be the last of winter or the first of spring. People from here go to northern New Mexico for skiing some years, and I-40 is on the southern edge of that. Similarly for the ski season in northern Arizona.
Even if it is still sort of winter, there can be plenty to see and do on the south rim of the Grand Canyon, and at the parks enroute (e.g. Petrified Forest).
Moab's spring begins in March, but the bigger off-roading gatherings are towards the end of the month. It gets busy enough that you should be thinking about firm reservations well in advance, last two weeks of March and into April.
I've used San Antonio and the Texas Hill Country as Spring Break destinations, if it is too early to go somewhere more local (like the Ozarks) that particularly year. That's because they are close for me. I've also used Nashville a couple of years, and the Smokies one spring when spring came early to the mountains. That's another direction for you.
