Not familiar with TUS, but if you get farther away from downtown, it will get cheaper.

In SLC, the valley is going to be cheaper than downtown or areas in the east foothills. West side of the valley is going to be cheaper. Southwest valley area is family oriented, but not much to do out there. Sugarhouse area has things to do, and is near mountains/skiing, but is pricier than some other areas...I'd probably look there or Holladay for starters unless you're a member of the dominant local religion.

You can go north or south as far as Ogden or Provo, but not much to do there and rush hour traffic to the airport would get annoying.

SLC is in the middle of a high desert...if you go far enough in any direction, it will get very, very inexpensive but again not much to do.