US-191 runs from Mexico to Canada, but the part that runs from Springerville/Eagar south to Morenci is referred to as the “Devil’s Highway” mostly due to the former designation as US-666 (the sixth spur off US-66). It is also designated as the Coronado Trail Scenic Byway.
Byways.org details

It is twisty, forested, and has relatively few vehicles on it. Perfect for motorcycles, but watch out for wildlife.

The steepest and twistiest turns are at the southern end near Morenci. That is why most cruiser groups, especially those with passengers, prefer to run the Devil’s Highway south-to-north and use the US-180 for the north-to-south, making it a loop.

This trip is not recommended for winter. Elevations up to 9000 feet, snow, black ice, and the remote nature of the road are conspiring against you. Late Spring and early fall are spectacular, but try to avoid the rain unless you plan to take it easy through the turns. The summer is a good time for the high altitude portion, but much of NM and all through Clifton and Morenci are really too warm. Run the 191 both ways, based out of Springerville/Eagar and you should be OK in summer.

There are a few towns on the US-180 portion of the loop, but there is really only 1 place to stop for services/facilities between Alpine (North edge of loop) and Morenci. Hannagan Meadow is a great stop along the route, with an outdoor seating area (with rockers) and indoor dining. As a lodge, it would also be a great base for several days of exploring the area as well as other activities (horseback riding, etc.). No gas, so stop in Alpine or Morenci to top off.

Leave yourself plenty of time to stop and enjoy the spectacular views and you will have a wonderful riding experience. National Geographic Scenic Byways description