I think Prescott would be just fine for you working around your necessary stay in Phoenix. Due to family we once needed to be close to Phoenix one recent summer. We alternated between Prescott and Flagstaff. Hope it works out for you.
Also, if you plan on returning to the Phoenix area a little later in the fall season or winter/spring, the regional parks are excellent places to stay. They are in various places circling the greater Phoenix area, have nice large campsites, great hiking and in scenic areas. We use them, along with Lost Dutchman when we visit the area.
Our favorites are McDowell Mountain, Usery, Cave Creek and Lake Pleasant.
Maricopa County Parks of the Phoenix Area