Hey, I was also accepted into the program at Utah. I declined but it was a hard decision. So far as I can tell the commutative algebra at Utah is about as good as it gets. Also I was told by a recent graduate that there is strong community of graduate students and that the city is very affordable. She said The Avenues is a neighbourhood in Salt Lake, biking distance from campus, where a lot of grad students live in nice old houses.
One negative I wasn't aware of is that Salt Lake has some of the most polluted air in the U.S. during the winters. This is due to this something called climate inversion which you can read about here https://en.wikipedia.org/wiki/Climate_of_Salt_Lake_City
. I've heard that inner city salt lake city is pretty progressive, but you should keep in mind that The State of Utah is essentially run by the LDS, so it's going to be very conservative in a lot of respects. For example alcohol is heavily regulated.