I love Prescott year round, where there are any number of hikes and bike paths in and around town. There's a mess of shops, museums, galleries, and restaurants here too.
As you enter the third youngest state in the republic from the north Monument Valley is awesome - culturally and geologically, as is Canyon De Chelly along the eastern border.
South of Canyon de Chelly is The Painted Desert and The Petrified Forest. West of there on the way to Flagstaff via Interstate 40 is Meteor Crater.
In Flagstaff Lowell Observatory is worth seeing and there are a mess of restaurants to try.
If you haven't been to The Grand Canyon that's easy to fix (and should be). There some fine accommodations there but you'll need to book stays in the park well in advance.
As my posts on FB and my blog suggest, we've been looking into the archaeological pre-history of the Four Corners region. There's a loop of sites in the Verde Valley we've seen most of called The Sinaugua Trail. There is also Agua Fria, Black Mesa, Tonto, and others...
Between Verde Valley and Prescott is the former ghost town of Jerome and a winding scenic drive through the Mingus Mountains.
As for points south... Even though it's crazy hot in the summer, a visit to Tucson should include at least a half day at the Pima Air and Space Museum. Haven't gotten down to Tombstone yet, but folks say its worth a visit.