I used to live on campus, from 2007-2010 to be exact. I lived in Shoreline Ridge, which is about 2 minutes on foot from the Medical School and Hospital. I lived there with my wife and two children.
Anyway, about two years ago the University of Utah HRE (housing and residential education) department decided that Shoreline Ridge would no longer be tolerating families. I say "tolerate" because that's exactly what they did for us from that point on until we all left. They made everything very uncomfortable for us, I assume to encourage us to vacate our apartments. As one family would finish up with their studies, they would be replaced with a single student. No families were allowed to apply for housing in Shoreline Ridge. At this point, there are about 140 apartments and a nice children's playground for single students to enjoy. Families are no longer welcome.
So the only option at this point for married students, or single students with children, is to live in the University Village (east and west), which is about a mile to the south, perched on the far southern edge of campus well away from the medical school and hospital. The Village consists of 40+ year old apartments which have no dishwashers, and no clothes dryer hookups. It's pretty grim compared to Shoreline.
The sad thing is that I know that there is a plan to demolish either the east or west village and not rebuild it, and then demolish the other and replace it with new housing. So there's a chance that if you do live in the Village you'll be evicted at some point to allow for either the demolition or demolition and new construction. The villages are also not off limits to single students, so you'll be competing with them to get an apartment, and if you do get one, it's one that was build over 40 years ago rather than just over a decade ago.
It's actually one of the reasons I didn't apply to the U of U. It's a great program to be sure, and I like the university overall. But it's housing department is extremely unfriendly to married students.
You can probably find a house or basement apartment to rent near campus, but the neighborhoods bordering the U of U are among the very most expensive in SLC (especially the one's near the hospital) so I can't comment on how much you might expect to pay.
Also bear in mind that the Salt Lake Valley has a great public transit system. You can ride the Trax train right to the medical school for free as a U of U student. And you can even ride the commuter train down from the cities north of SLC for free with your student ID.
Although there were some good points made in this post, a lot of this information is incorrect. I have lived in married student housing (east village) for 3 years now and have found it extremely "family friendly."
Saying that the village is "well away" from the medical school and hospital is a bit of a stretch. I often walk to my lab (located at the hospital) and it takes about 15 minutes. Better than that, there are shuttles and busses that can get you there very easily throughout the day.
Dishwashers don't come standard, but they are easy to come by from other families moving out, and they are very cheap and easy to set up. There ARE hookups for washers AND dryers in the apartments. The caveat is you have to have a lower voltage dryer. Once again, they are cheap and easy to come by from families moving out of the village.
There is no getting past the age of the apartments (they are very old), but they are plenty nice enough to live in, especially considering the family-friendly environment you are surrounded by. The rumor about knocking down one of the complexes has been circulating for 10+ years now. Eventually? Probably. Any time soon? Probably not.
Finally, I believe preference is given to Married students. So if you apply a couple of months in advance, you shouldn't have a problem getting an apartment. e.g. I applied in March, and had moved in by May.
Anyways the previous post was right in saying that trax is very convenient and goes right to the hospital, so it would be easy to find an apartment off campus and a convenient commuting route. It would not, however, be as cheap. Student housing is very cheap and includes everything from electric, water, internet (very fast), basic cable, and a great environment. And you won't get much more convenient as far as location.
Just wanted to clear those few things up for those wondering. Always good to have more than one viewpoint.