Well since it looks like you'll be heading west mostly on I-10, if you get a chance to head further south and visit the Florida Keys, and the Everglades prior to your trip West, those are great places. Right now there's construction around those areas but if you are not in a hurry and you have good mapping skills some advance planning can help you avoid some of it. There's also Cape Canaveral which is astounding in its own right.
As you head west, there are historic Civil War battlefields further north of I-10 in the Southeastern states, you can visit New Orleans, LA, then in Texas there's beautiful Austin and historic San Antonio in Texas, the hill towns of Johnson City, the NASA center in Houston.
In New Mexico there is White Sands National monument, the Carlsbad Caverns, the Sandia Mountains in Albuquerque, the capitol city of Santa Fe and the Art communities of Taos (but there will be snow about the time you get there) Albuquerque, Santa Fe and Taos are north of I-10 quite a ways (use I-25 to get there quickly).
Arizona also has Tombstone on the way to Tucson, then from Phoenix, northbound to Sedona and on to Grand Canyon) northbound of I-10 using I-17.
Well there's just a few more suggestions. I need to stop now, I'm getting real tired from this long vacation. I might have to stow away in your rig if you get this going cuz the route alone sounds like fun!!