If you're going to be there for a while, you do need to find an area where your kids will have a "critical mass" of non-LDS friends and classmates. You and your wife can selectively avoid negative aspects of LDS, but your kids will not have that option in a haevy LDS neighborhood. It's fine under age 5, but after that it will rear it's ugly head. Not any kind of institutionalized exclusion, but it will naturally manifest as the kids get old enough to realize the difference between those who go to the church and those who don't. Some parents will subtly encourage their kids to steer clear of non-LDS. It will be rough on the kids if you don't find a diverse area...they will end up feeling like outsiders, which may lead to outsider behavior (goth, rebellion, crime, etc).

Park City is a different world, no worries there other than the pass. Holiday is somewhat diverse, with easy access to 80E and the various canyons so it attracts a lot of outdoor types (often transplants from other states). Sugarhouse is the eclectic gay/academic neighborhood, but rather pricey for what you get IMO. The avenues has the same flavor but I suspect the schools in that area are too LDS. Stay the hell away from West Jordan, Draper, Sandy, Bountiful, etc.