As a non-LDS person, along with being a minority (Asian) and growing up in Utah (and still living here), don't believe half of the stuff the posts above tell you.
1) SLC proper is demographically approximately 50% LDS/50% non. The city itself has a Democratic mayor, the 2nd Congressional district, which basically encompasses SLC has a Democratic representative (along he's a Blue Dog). Things are open on Sundays, which is great, since most LDS people don't shop then, it's a great time to get your errands done. Along with that, the west side of town, along with its suburbs, is significantly more diverse than the east side.
2) The suburbs are distinctly much more LDS than the city proper. However, unless you're big in to city politics, does it really matter? I live in a suburb of SLC (Sandy), and yes, the local politics are dominated by LDS members. However, it's not like they're forcing you to go to church, and they're definitely not forcing you to interact with them. We get the occasional missionary knock and door flyer for activities at the local church, we just choose to either tell them "no thank you" or don't go. It's not that hard to get a support network of friends who are not LDS. And despite what some may say, there are cool LDS people in the state. My best friend from childhood that I've now known for about 30 years is LDS. I just know what the limits are of doing stuff with them. If I want a drink, I call up other buddies to go with me.
3) Many states outside of Utah have both "weak" beer at 3.2% and state run liquor stores. The liquor laws are a little bit quirky, but getting a drink isn't as hard as it's made out to be. Laws have become much more liberal since the Olympics.
4) Outdoors activities are great. Skiing/boarding, hiking, mountain biking are all easily accessible. If you're a roadie (as I've turned in to) SLC is NOT the friendliest road bike town out there. You'll find narrow shoulders and a$$hole drivers.
5) Despite what mercanucaribe said (who had been here 2 days), Salt Lake is actually quite green and lush, much to the dismay of the water districts here. We use, per capita, more water on our lawns that any other city in the Intermountain region. The mountains are quite green all season long, with the exception of the grasses, but that is to be found in any other local climate such as southern California.
The long and the short of it, is SLC is just like any other city. I've lived in other towns for extended periods (years) of time such as the Bay, and have always come back to SLC. At this point, it's a modern metropolis (1.5million in the metro area) offering every amenity that you'd find in a NYC, LA, or SF. Some of it may be a little harder to find, and just like any locality, there are certain local rules/regs that you must follow, but it's not like there are hundreds of polygamists walking down the street (I've seen them maybe 20 times in my lifetime here) and missionaries kicking down your doors to convert you.
If you're going to be making a good salary, like the outdoors, and generally treat people the way you want to be treated, you'll be fine here, there, or anywhere. I'd encourage you to come as the cost of living is generally low compared to other "large" cities and if you're making bank, you'll be able to have an extremely good time here.
/end of my tourist board spiel