If you go through Arizona via Route 66:
https://roadtripusa.com/wp-content/u...06_Arizona.jpg
then making a reservation for a couple of nights within the Grand Canyon is a must Grand Canyon National Park Lodges - You're Not Just Close - You're There!
The Grand Canyon has crowds in the summer but the majority do not have reservations at one of the lodges so it is still quiet at sunrise and sunset (and they are magnificent to view) plus I find that wildlife is just more active at dawn and dusk. There is no hunting in this park so it is overrun with elk and it is fun to watch them enjoying the grass that has been cultivated in front of a couple of the lodges (they think it's there for them). If you like to hike--this is a great place for it.
I also like Oak Creek Canyon, Sedona and Prescott--all have good hikes but great views via your car too.

I-10 Arizona Map
Near Phoenix (Mesa actually)--I always enjoyed Tubing the Salt River
http://www.saltrivertubing.com/directions/
Of course, it has to be late Spring/Summer/early Fall because this river is cold (the source of this river is melted snow) but feels great because it gets so hot in this part of Arizona.
Tucson is a must see. There's Sabino Canyon Seven Falls Trail - Arizona | AllTrails.com (that's a fairly easy hike but if you are adventurous -- Mt. Lemmon Ascent - Tucson Trail Runners -- Every Spring my AFROTC unit hiked this one from 2750 then camped out on top when we were done, it is very challenging 2750 - 9100 ft ascent and 18 miles of trail - wonderful views -- you can also just drive from Tucson to Mount Lemon -- a very scenic drive. Beware, the parking in Sabino Canyon fills, especially on the weekend, even very short hikes and bike rides are very satisfying there. The desert in Tucson is not barren--there are many scenic drives https://www.go-arizona.com/Tucson/Scenic-Drives/

Of course their are other great places between Route 66 and I - 10 (Arizona is a hiker's paradise) but I assume that you just be spending a few days there....