If by non-Mormon you mean most liberal and containing the most diverse people, I'd suggest Sugarhouse. However, anywhere north of 5000 south in Salt Lake County would have the lowest percentage of LDS church members.
Mormons tend to stick to the south end of the Salt Lake Valley and Utah county in the newer developments, which are more conservative and family-oriented. There will, however, probably be several LDS members in your neighborhood, no matter where you live.
I am a Mormon who has lived in Salt Lake City my whole life - there are no neighborhoods in Salt Lake that don't have any LDS people in them. However, if you are looking for a more liberal neighborhood with a low concentration of church members, Sugarhouse would be my first suggestion. My second suggestion would be the Avenues. There will be a few (maybe 15-20%) LDS people in your neighborhood, but they will be the more liberal sort.
Anywhere on the north side of 5000 south in Salt Lake County will have a lower concentration than the southern part of the county. The southern side has larger homes with a slightly lower cost of living - much more friendly to church members with large families.
Salt Lake City
Salt lake city
The Mormon Tabernacle
Salt Lake City is in Utah.
The Mormons or Church of Latter Day Saints were forced our of Illinois by the Mormon Wars. Many were upset by the Mormon idea of plural marriages. The Mormons took their belongings to Nebraska and moved to Salt Lake City in 1847.
Salt Lake City, Utah is considered the end of the Mormon trail.
The Mormon Pioneers arrived and began to settle Salt Lake City in 1847.
No, in the actual city of Salt Lake City, about 30% of the population is Mormon, possibly less. Within the state of Utah as a whole, about 60% are Mormon.
Salt Lake City, Utah.
Salt Lake City was started by a group of several thousand Mormon Pioneers. The man who directed much of the city planning was Brigham Young, the president of the Church of Jesus Christ of Latter Day Saints (commonly called the "Mormon" Church) at the time.
There are several bars in the Salt Lake City community.
Mormon Lake