Do you have a special reason for Prescott? Cottonwood State Park in Cottonwood, AZ would be our choice. It's a good area for exploring Indian ruins and also Sedona. You could even do a day trip to Grand Canyon but a long day.
For Prescott or wherever... take Hwy 89 north out of Flagstaff, AZ and pick up 160 at Tuba City, AZ to Kayenta. Then pick up 163 north and stop for Monument Valley. Then continue north on 163 to 191 to Moab.
You'd then have to backtrack on 191 south to 491 to 160 across southern Colorado - Mesa Verde Nat'l Park at Cortez, Durango and Pagosa Springs for a wonder soak.
From Pagosa Springs, CO take 84 south to 64 east into Taos.