Although the map shows the route through Queen Creek and Casa Grande, you can save time and head directly for Tucson from the I17.
Queen Creek is at the south east edge of Phoenix and hosts numerous horses shows.
Casa Grande is literally a desert town with blowing sand storms. Eloy makes a good fuel stop with a big truck stop. Tucson has its own sights to see, including the U of A.
Tombstone, Arizona is a historic town that is fun to visit, especially with horses. There are great stalls and RV hook ups available at the Tombstone Livery. From their stalls, you can ride across Wyatt Earp country into town. The main street is blocked off from cars, so once you arrive in town it's just horses, tourists and the stage coach. Sierra Vista is the closest town with a variety of supplies.