Along the Mogollan Rim north of Payson is really pretty. It's a massive dropoff where teh Rockies fall to Mexico. Really spectacular when a storm rolls up the Rim.
It's Apache/Sitgreaves and Coconino National Forest. There is a road that runs all along the Rim (aptly named Rim Road) from highway 87 in the West to the Payson Heber Highway in the East. There is a campground with showers at the East end. 15 years ago I ate at The German Cowboy in PAyson a fair amount. Okay, drank a lot, but I think the food was decent. Of course, I was getting in to town every two weeks and living in a tent, so who knows. You can also run up 87 to its intersection with I-40 and stand on a corner in Wnslow Arizona. Truly, such a fine sight to see.
Also, if you go up past Military Sinkhole through Hole-in-the-Ground, you might see GSS as Poon Tank, or Marc at either Sheep Creek or Mule Spring.