I'm from Utah ~ born and raised and still here.
And I'm not a Mormon, and I have a drink whenever I want (Long Island Iced Teas and Jack Daniels with Coke are some of my favourites!). The liquor laws
are a bit odd ~ you can't have more than one alcoholic drink in front of you at the same time ~ but don't hold it against all of us...we didn't make the law, and we're not fond of it, either.
Your trip to Salt Lake will not be a horrible one, if you don't want it to be ~ there is plenty to see. Up by the Capitol is so pretty ~ lots of history there. The University of Utah is nearby; a wonderful campus, and the Hogle Zoo is nearby as well, as was mentioned before. There are some crime and gang problems, in certain areas, like most big cities...but it's not a bad place to visit. If you didn't see the Temples here and there, you'd forget you were even in Mormon country...and I think the Temples are pretty to look at, no matter what your faith. The Mormons don't jump out and grab you, and force you to come inside.
Have a good time on your trip!