From someone that moved here 8 months ago, Utah seems to be a bad place for people that want to party, so you're in luck there. Tons of biking (mountain / trails). Shooting on public land is okay in many places, not restricted to a range.
Sugar House is city living but decent area, as is the Avenues. Bountiful is nice too. You will have lots of options based on your budget.
As for the Mormons, my wife has been shunned by many of her college classmates because she isn't of the same faith. I find this quite funny because we are Baptists, attend church on Sunday, and try to live by the Bible. I cannot really comment as I am extremely quiet and rarely talk to anyone. While there are a lot of Mormons, there are a lot of "others" as well. I don't think you'll have any issues meeting people.