OK. Around Phoenix/Mesa:
Mesa Southwest Museum
San Carlos Apache Reservation
Superstition Mountains (Lost Dutchman's Mine)
Tucson is about two hours away:
Old Tucson
Tombstone (Boot Hill, OK Corral)
Bisbee (restored ghost town)
Saguaro National Monument (like a national forest, but with Saguaro cactus)
Arizona Desert Sonoran Museum
There's lots more, but this is off the top of my head.