Not too far off the scenic route. The country you go through on the way is lovely – it’s US 60 between I-25 and I-17, or skip I-17 and stick on Arizona 260 to either Camp Verde (nice pre-Columbian site near Camp Verde) or north from Payson up to Lake Mary and from there to the Canyon. My preference is to go to Williams and take the scenic railway to the Canyon, but you can also drive there. Parking ain’t cheap, but neither is the railway.
Between I-25 and Pie Town you cross the Plains of San Agustin with the VLA radiotelescope, then some pretty hill country[1], Pie Town (pop. 186, but some good cafes and pricey but award-winning pie. Do try the apple/pinon/green chile one, it’s awesome and not significantly picante.) After Pie Town, it’s more pretty country of a very Western sort, running an altitude of around 7500-8000 feet. Quemado is nice, small, but has a good cafe (the Largo) and next is Springerville. Springerville has several modest restaurants, nothing special, but decent fuel prices (don’t plan to fill up between Socorro and Springerville) and you can either go west on US 60, jog south and then west on AZ 260, possibly some nice side trips off of 260, or west a bit on 60 and then north on 191 to I-40 or on towards Navajo country.
60 west from Springerville is OK, but I’ve driven it too many times to like it much. Plenty of recent cinder cones and lots of cattle. Either 60 or 260 will get you to Show Low, lots of restaurants and the cheapest fuel you’ll see before Payson. From Show Low, head NW towards Heber. More high plains, forest, etc. and after Heber you’re on your way to the Mogollon Rim and Christopher Creek. Absolutely DO take this stretch in daylight, not because it’s dangerous (twisty, but not hard) but because you’ll be going down the Rim and the view is amazing. Just before 260 goes down the Rim, there’s a visitor center/viewing site on the south side of the road. Great place to take a break and breathe clean air and … well, you’ll see.
From Payson you can head over on 260 to Camp Verde (above) or north towards Pine and Lake Mary. Near Pine there’s a truly awesome travertine bridge over Pine Creek, with a park etc.
[1] If you skip Pie Town for Reserve, fork off 60 at Datil and head southwest through some lovely valleys and ranches. Reserve west takes you to Alpine, then north on 191 to Springerville through dense forest.