Here's an old story:
A guy that works as a salesman for a company is told they're having a contest to see who sells the most. He asks, "What's the prize?" His boss tells him, "First prize is a week in Salt Lake City." "Really," says the salesman, "what's second prize?" "Two weeks in Salt Lake City!" says his boss. :)
If you only have one day, you're probably not going to be able to take advantage of the best thing in SLC, the skiing. Most of the good places are 2-3 hours outside the city, in the mountains. You could, but you'd have to rush and wouldn't get much skiing in.
You can go tour the mormon temple complex, but be careful -- don't put your name and address in the "visitor book" or you'll get visited by the mormon missionaries when you get home, and they're very agressive.
Lots of good places to eat, but avoid Chinese or Thai food -- I've never found a good restaurant for either of those in SLC.