Once you get to AZ...
There are a few fires burning now, so some areas may have fire crews and smoke.
From Flag take 89 up to the east entrance to GCNP and follow along Rim Drive, stopping at lookout points. In the Village head up to the rim and walk down Bright Angel Trail for a mile or so - well worth it. Then take 64 and 180 back into Flag.
From Flag take 89A down thru Oak Creek Canyon into Sedona. Stay on 89A over thru Cottonwood (you can stop at Tuzigoot) and continue on into Jerome. Come down Mingus Mountain into Prescott Valley and take 89 into Prescott. Check out Whiskey Row. Stay on 89 down Yarnell Hill into Congress. Then you can turn around - those roads are worth riding again, or take 71 to 93 and head up to I-40 and east to Williams.
Check out Route 66 in Williams.
Grand Canyon Harley (in Bellemont, between Williams and Flagstaff) often has stuff going on over the weekend. They are right off of 40 (exit 185).
West of Williams you can get back on old Route 66 in Seligman and take it thru Kingman into Oatman.
Walnut Canyon is worth a look and just east of Flag off of 40.
Take 40 east of Flag and you can visit Petrified Forest.
From Holbrook (along 40) take AZ-77 S for a couple of miles to AZ-377 S to AZ-277 S into Heber-Overgaard. Take AZ-260 W along the Mogollon Rim to Payson (it will be warmer there) and then up thru Pine and Strawberry. Great pie at Strawberry Lodge.
Just north of there you can turn left onto 260 (General Crook Trail) and head over to Camp Verde and north on I-17 to Montezuma's Castle (cliff dwellings).
Or you can take 87 (by not turning onto Gen Crook Trail) and head up thru Happy Jack to Lake Mary Road and take it back into Flagstaff.
Another great ride - perhaps the best in the state - would have you take I-40 east of Flag to Holbrook and head on 180 down to St Johns. From there take 191 down thru Springerville and stop in Alpine (~9,000'). From Alpine down to the mining towns of Clifton and Morenci is a wild ride. This is the Coronado Trail. Up until '92 it was US-666, the Devil's Highway. Very twisty and few guard rails.
It will be warm (maybe even hot) down in Morenci, so fuel up somewhere and either turn around or take 191 over to 70 into Safford and on up into Globe. In Globe take US-60 / AZ-77 north up thru Salt River Canyon into Show Low.
From Show Low you can stay on 77 to I-40 and west to Flag or take 260 west back into Payson and north from there.