I second the option of Hwy 89 northeast out of Flagstaff, then west on Hwy 64 just south of Cameron, AZ. I prefer this route as it is less traveled and wide open scenery. From the south on Hwy 64/180, it is a slow rolling parking lot with semi's, motorhomes, campers, tour buses, etc etc etc.
Another option since you're coming in from the east, take I-10 west until you hit Lordsburg, NM. Take Hwy 70 west towards Duncan, AZ, then split off northwest on Hwy 75 towards Three Way, turning right (north) to Clifton/Morenci. Make sure to fuel your beast up before leaving these mining communities!
Take Hwy 191 north to Alpine (88 miles, 3 hours, fuel up again), then either stay in Alpine for the night or continue north to I-40, or head west on Hwy 60 to Eagar-Springerville Pinetop-Lakeside, or Show Low if the light is fading. From any of these communities, you can easily head north to I-40 then west into Flagstaff, or take any of the Indian Highways north of I-40 towards Cameron, AZ, which is northeast of Flagstaff.
If you've ridden the Dragon, then you understand it's hype and allure. But after riding the Coronado Trail, aka Hwy 191, aka the Devil's Highway aka Hwy 666, then you'll understand why this little twisty road puts the Dragon to shame. But be warned, it'll definitely put a strain on your mental awareness due to the technicalities in riding this under rated two-laner in the middle of nowhere.
Following is a video pulled off the internet, 9 minutes in length. It is an average depiction of riding most of the 88 miles, which holds so many curves and twisties, it is nearly impossible to maintain an accurate count. I wasn't impressed with the riders driving behavior, but when taking on this roadway and trying to ogle the scenery, it is easy to get lost in your own lane.
https://www.youtube.com/watch?v=8PcCs7a6P_k
- David