Do you have children?
Anyone from Utah (which I am) would probably tell you to go check out Temple Square. Even if you are not a member of the Mormon church it is still a pretty amazing place to check out. I would also recommend the Family History Library--you would be amazed at what you can find out about your ancestors and there are lots of volunteers that would be more than happy to help you. There are also free concerts there on a pretty regular basis. Directly across the street from Temple Square is the brand new Gateway Mall. It is a fabulous addition to the city--it is an open-air type mall.
There is the Hogle Zoo, the Clark Planetarium, just a little South of SLC there is Trolley Square where there are some really neat gardens, a natural science museum, some water features, and a theater. This is the Place Monument is an old fashioned pioneer outdoor museum (people in period costumes, chances to see what it was like to be a pioneer).
The Great Salt Lake can be fun. I have never been, but some of my other family have gone and seen it.
How long will you be there?