Yea...mormons here, outside of some rare exceptions, do not date or associated with non-mormons. Just the nature of the beast. There are a ton of Aryan chix all over though.
I'm currently over in Park City, which about a 45 minute drive from Salt Lake. If you have time I'd some come up here. Short story is that it's a rich, snobby, ski town, but it does have a cool main street with some good bars and restaurants. Chimayo there is fantastic, but expect to pay rich ski-town prices. No Name Saloon is the most popular late night bar and drinking spot, but a little shitty dive-bar next door O'Shucks is where you can find me hanging out many days. Not sure when your 2 weeks are, but ski-season may be in swing, if not try renting a bike.
This place is "in" Salt Lake too,
Log Haven - Utah's Best Restaurant, Wedding and Reception Venue great food, a bit higher class. Otherwise most of what I know is small divey places. Alex recommendations are good though I don't get in to Salt Lake much, may actually have to try that Pig in a Jelly Jar thing. Also on my list there:
Keys on Main: Nightlife. It's a dueling piano bar where the artists play for money. So if I put on Justin Bieber for 20$, 21$ makes the pain stop. Gimmicky but draws all ages and it is actually a fun, rowdy, and lively environment.
Brewvies: A movie theater that serves beer and food. Probably nothing insanely special about this place though I support it because the mormons try to shut it down every 2 fucking weeks because of the movies they show. Has little dive bar attached.
Beer bar: lots of good beer, open hall style place. Never been at crazy hours of the night but loved the beer selection and specialty dogs/burgers,
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