You have many options depending if you want interstates or secondary roads, as we would do.
1) From Fayetteville, Arkansas take 412 to I-35 north to I-70 west thru Denver to 191 south in Utah to Moab = 1155 miles
2) 412 to I-44 to OK City to I-40 west thru Albuquerque, NM. Then north on US491 at Gallup, NM to Cortez, CO to 191 north at Monticello to Moab = 1142 miles
3) 412 west to Hardesty, OK to US64 west to US56 for a short time picking up US64 again thru Taos, NM to 84 north into Pagosa Springs, CO and 160 west is 1062 miles
4) 412 as in #3 to US64 to I-25 north in NM/CO to 160 west to 491 to 191 north is 1061 miles
There are more options, too. It just depends what you want to see along the way.
We've driven all of the above with our 40' motorhome and we would choose secondary roads over interstates any day. It's just more pleasant driving for us and we see more.
Full-timed for 16 Years . . .
Traveled 8 yr in a 2004 Newmar Dutch Star 40' Diesel
& 8 yr in a 33' Travel Supreme 5th wheel