Yes, getting off the interstates in the West is very doable for your 21'. We did it all the time with our 40'. :) Go to Camping World or order online through the publisher 'Mountain Directory for Truckers and RVers'. Ordering through Amazon is extremely expensive for some reason. It'll make it easier for you to decide what roads to stay off. Many of the mountain roads are just fine for RVers.
You do have a big trip. How much time are you allowing? I'm sure you're aware that once you reach the southern Utah/Arizona area and all the way back home, it's going to be HOT if this trip is being planned for the summer.