Probably a 12 hour drive with few stops. You have 2 route choices. I70 to Utah, south to Moab on US 191 to US 163 to US 89 to AZ 64. You go through Grand Junction CO, Moab UT, Monument Valley etc.
The other route is I25 south to I 40 then from Williams up to the Grand Canyon. This route takes you south to NM, visiting Santa Fe, Albuquerque, Petrified Forest, Flagstaff Az.
If you are driving this far, I would spend more than one day at the Grand Canyon. Then head on to Vegas.
Woody Creek would be a long side trip on the first route I told you about.