Might try Cottonwood Heights just at the mouth of Cottonwood canyons. I have a buddy that lives in the area and it seems pretty diverse, its really close to the freeway, and just down the road from some major resorts.. There is going to be a big LDS influance anywhere you go but it will be more prominant in Davis County, the outer regions of Salt Lake County (Draper, West and South Jordan) and of course Utah County (hated every second that I lived there, and I'm LDS). Sugarhouse and Holiday are also very nice areas with alot of cultural diversity.

With the large LDS population you will run into some bad eggs who will treat you like you are below them, and won't let there kids hang out with those who are not LDS but for the most part they are just normal people and treat you the same.

If you go the Park City route Parley's Canyon usually isn't a problem since Utah has so much experience with the snow but there will be times when it completely shuts down because of the snow. It all depends on the type of snow we get that year, we had alot of people calling us in ops because they weren't going to make a flight due to Parley's being at a standstill.