Temple Square is the physical capital of the Church of Jesus Christ of Latter-Day Saints. Its gardens and buildings are tourist attractions regardless of your religious affiliation. At minimum, you need a photo here to let folks know you've been to the Beehive State.
This state icon is in Southern Utah and requires 1-2 days for proper travel and viewing from Salt Lake City. However, if you wish to make this trip a vacation, Utah is home to at least four of the United States' national parks. The Delicate Arch is worth the trip, and hike to see it. Simply beautiful.