Yarnell/Peeples Valley, Wickenburg, Prescott, Jerome (wish I could live here), Crown King, Mogollon Rim, Verde River near Camp Verde for camping/swimming.
Payson's got some really pretty country and your not too far from Lake Roosevelt or the Mogollon Rim.
I remember as a kid visiting my grandparents there and me and my cousins going jeeping or riding out in the woods, it was really cool.
Paige has to be one of my favorite places to visit. Jerome is nice, Sedona too commercial but if you are into buying gifts, great place to buy Oak Creek is nice too a bit less crazy than Sedona. Skull Valley is cool, not much there, I guess that's why I lime it. Black Canyon City where the Saguaro begins coming down from Prescott area.
Scottsdale and Tempe were the last places in AZ I visited. I stayed in Scottsdale and worked in Tempe. I liked both.
I enjoyed Tuscon (35+ years ago). I liked driving out to the desert. I also liked going to the top of A Mountain. 100 deg. at the base and 60 deg. and a little snow at the top.