Steve, two choices:
#1
Clifton/Morenci up the Coronado Trail to Hannigan's Meadow then Eager/Springerville
119 miles, 460 turns, many posted 10MPH, and mean it. Excellent scenery for a passenger but the driver may not want to get distracted
#2
Clifton then NW to 180N. in NM, up to Alpine and Eager/Springerville
Still plenty of turns and elevation changes, just more sweeping and higher speed. It's my choice, but then, I've not had the best of luck on the trail
You should certainly do The Trail, if you never have. After driving it a few times, perhaps give the NM route a try for a different type of fun. My 2¢