You can also get in touch with the bicycle coordinators for Utah and Arizona. Many have online resources as well as printed materials. Nearly every state publishes a bicycle map of some sort that they will send out for free and the coordinators often have more information they can distribute for no charge as well. And while the maps aren't as detailed as ours, they generally offer suggested roads for cycling through their state. Here is a link to the contact information for all of the bicycle coordinators and some online materials: http://www.pedbikeinfo.org/data/state.cfm
For more tips and ideas on how to create your own route, see this blog post on the topic:http://www.adventurecycling.org/resources/blog/how-to-create-your-own-route/
For lodging, once you have determined your route, you can look at state tourism sites. In Montana, the tourism site lists towns and accommodations.
Since Utah and Arizona have smaller populations and less roads (as compared to states in the east) you'll most likely ride on U.S. and state highways with variable shoulder widths, and not county roads. It's possible you can ride on the interstates also, if you want to do that. They at least have wide shoulders. But check with the state bicycle coordinators to see if it's allowed. And I bet SLC and Phoenix have bike maps, google each city and see what comes up.
You can also go to crazyguyonabike.com and review online biking journals. Search to see if anyone has written about riding from SLC to Phoenix.