I don't really understand all the discussion about mountain roads. If you want to see the good parts of America you just have to learn to deal with it. It is more tiring than driving flat straight roads, so just make your first few days pretty short. Contol your speed and pull grades in the right gear. Do not ride your brakes. Watch your temp gauges and you will be fine.
I used to drive through southern Utah twice a year for a job on the Navajo Res. There is nothing special about any of those roads including US 89.