If you head to SLC, you'll probably be taking I15 North if you're coming from AZ. The mountains will probably be thawed enough to make the Mount Nebo loop, which is a pretty scenic byway in the middle of Utah (near Payson). Once you get to Provo & SLC, the wasatch front is an impressive mountain range. There are many canyons to venture up with hundreds of trails (and geocaches). A few places of note: Mount Timpanogos near Provo has a world famous cave. After a mile or so hike, you'll reach the entrance. This cave consists of a guided tour through one of the most unique caverns around. Another great place to travel is the Big and Little Cottonwood canyons to the east of SLC.
If you come from CO and travel farther north through Wyoming, you could come to SLC via the high Unita mountains. These are probably the most impressive mountains of northern Utah.
Hope that helps,
Azkul
My Nature/Landscape Photo gallery - http://www.thelensflare.com