I was born and raised in the Salt Lake City area. It's an embarassing omission but since that is the case and since I applied to the University of Utah's graduate program, I figured I could shed some light on the area and the school.
Admitedly, the University of Utah doesn't have the most well rounded program. They work almost exclusively in one of two fields, Condensed Matter or Astronomy/Astrophysics with a bit of dabbling in biophysics (virus budding, molecular motors). Their CME groups tend to work a lot with NMR, spin electronics and hyperpolarized gases. The astro department does a lot of high energy astrophysics/cosmic rays and a fair bit of observational astro in galaxy/planet/star formation. The University of Utah went through a fairly significant hiring phase in roughly the last year and it was done almost exclusively for their observational astro department, so many of the research groups in astro are fresh faced and rosy cheeked.
If you happen to be interested in comp sci applications in physics, the University of Utah has The Scientific Computing and Imaging Institute
which does a lot of pretty neat cross-disciplinary work with the other science programs, including physics/astro.
I've left the best for last, however, because what many don't realise about the U is that they have an astoundingly good CMT program. Most of the research seems to focus on spintronics, disordered electronic systems and strongly correlated electrons. The CMT faculty are frequently referred to by the grad students as the Russian Mafia (Alexei Efros, Eugene Mishchenko, Vagharsh Mkhitaryan, Mikhail Raikh and Oleg Starykh) and I'm told that it is thoroughly amusing/humbling (depending on whether you are listening to the talk or giving it) when they start asking questions.
Utah is technically a desert but, despite this, the state experiences all 4 seasons and it experiences each of them to their extreme. Winters are very cold and we get lots of snow while summers are very hot and dry. If you enjoy outdoor activites, there are very few places that are better to go than Utah. Of course the state is famous for its snow which provides world reknowned skiing and snowboarding, but it also has great hiking, biking, rock climbing and camping locations. In terms of water sports, the Great Salt Lake is useless but the location does give you relatively close access to both Bear Lake and Lake Powell. Arches national park, Zions national park, Bryce Canyon, Goblin Valley and Capitol Reef are a few more great scenic areas that are only a few hours drive from SLC.
Utah has mormons and lots of them. With that said, Salt Lake City has been the location where all of the non-mormons tended to congregate for quite a while and this not only makes the area significantly more liberal than the rest of the state, but it has also fostered a fairly significant counter culture. I think it's probably fair to say that Salt Lake is to Utah what Austin is to Texas (i.e. Keep Austin Weird). All of the good bars and brewpubs also tended to pool in the downtown Salt Lake area so being at the UofU gives you close access to some award winning breweries like Wasatch Breweries, the Uintah Brewing Company and the Epic Brewing Company.
Living in the Salt Lake area is very affordable. You can typically find studio apartments or 1 bedroom apartments for as low as $400-$500/mo, although these apartments typically require you to commute a few miles to get to the campus. A number of the current grad students live in nearby or on campus housing and rather than owning a car, utilize the local public transportation bus system and TRAX light rail (all students get free year round passes to use both of these services). The only major advice I can give when selecting an apartment is to stay on the east side of I-15. Although typically cheaper, property on the west side tends to be older and in less desireable neighborhoods.
Park City is only about a 20 minute drive from downton SLC which is great if you like to ski and really convenient if you want to go to the Sundance Film Festival (i.e. you don't need to pay for the expensive nearby hotels). Las Vegas is also relatively nearby (roughly 7-8 hour drive along I-15 South).
This is everything that comes to mind right now but I'm willing to answer any and all questions about the school and the area that you can think.
Oh, and for the best pizza you'll ever have go to Rusted Sun Pizzeria
on State St. If you are looking to relax and have a beer, check out Brewvies Cinema Pub