This is a long list, but here a few items...

Drive the Apache Trail (Apache Jct. to Roosevelt Dam)
Spend a night at the Shady Dell in Bisbee
Spend a night at the LaPosada in Winslow
Visit Saguaro National Park in Tucson (and Tucson's 4th Ave.)
Visit Canyon de Chelly
Visit the Lowell Observatory in Flagstaff (and Walnut Canyon)
Visit Boyce Thompson Arboretum State Park (near Superior)
Spend a night in a yurt (or cabin) at Lyman Lake State Park
Visit Palm Canyon in the Kofa National Wildlife Refuge
Drive Route 66 from Seligman to Kingman to Oatman

More ideas at...
http://azfoo.net/places