In addition to the two sites mentioned above, I'd suggest Sunset Crater and Wupatki National Monument which is focused on a volcanic eruption and ancient Native American ruins. It's just north of Flagstaff on Hwy 89.
Wupatki National MonumentAnother fine site is Walnut Canyon which is just a little way outside of Flagstaff (South of I-40).
Walnut CanyonAll of the sites mentioned above may have problems with accessibility in January if there has been significant snowfall. Check Arizona road conditions here:
Arizona Highway Conditions