The University of Utah does NOT guarantee on-campus housing for scholars. On-campus housing for scholars is available through University Student Apartments. They offer single apartments and family housing.
Off-campus housing can be an affordable option as well. Resources for finding an apartment include KSL classifieds and Craig's List. A studio apartment (the most basic option available) will cost between $400-$650 per month. Be wary of any apartment listings that are less than $300 per month without roommates - often these are scams.
International Student and Scholar Services has also prepared a Scholar Housing List containing apartments close to the University campus. Check with the manager of the apartments for vacancies and application process.