Bike Route to Salt Lake City

Sounds like an adventure. Here is what I would recommend. I have driven 89 before and it is a beautiful and relatively quiet road.
http://www.mapmyride.com/route/us/az/grand%20canyon/524124577627575...
No Moab but Zion and Bryce probably make up for it.

This user's post has been ignored.

Another recommendation in order to pick up Moab is to take 191 South to 163 and 160 then onto the Canyon.  This puts you through Monument Valley.  Spectacular views!  Not much support along the way but some good roads with shoulders.  The reservation does have some sketchy areas but doable.  If your on you way North again then skip the South rim and loop to the North side.  I like it better over there anyway and a lot less traffic.  Have fun.