David and Paul are right bu they are sending you many hours out of your way. You can see the little painted desert by driving a little ways out of winslow and taking the exit for Second Mesa-I can't remember the road number-and driving for about twenty miles. Beautiful and NOT over photographed.
COnsidering your time line this is how I would go. Drive out of Phoenix turn onto the road that will get your to prescott. Drive over the hill to Jerome and then towards sedona and up oak creek canyon to Flagstaff. Your shots are going to be between the interstate and Prescott between prescott and Jerome, and in jerome if you like funky houses. Then outside sedona but it is not my favorite place. I love the drive from sedone up schnebly hill road but I forgot to mention you would need a 4x4. Skip sedona and drive straight into Oak Creek Canyon. Lovely shots abound if you get out andf walk around. I am not sure if it is still happening but you used to have to get a permit to park on the side of the road in oak creek canyon. Then to flagstaff.
GOing through salt river canyon to phoenix is foolish but you could get back to phoenix through Payson. This will take you over the Mogollon Rim.
Just my two cents having lived in NA for a number of years
PS sorry I am terrible with road numbers and names. The interstate is the one going north. I think the road to prescott has the word cherry in it. It is maybe 45 minutes out of phoenix. If you want more specific stuff I can find it.