Depending on where your interests lie, visiting Salt Lake City at any time of the year can be a rewarding and pleasant experience. If you want to see the sights, then it's a good idea to come in summer when the weather is at its warmest, while if your interests lie in skiing in the nearby Wasatch Mountains, then travel to Utah between November and March when the snow is at its best.
Because so many Mormons visit the city in order to see the sights, it can be a good idea to avoid travelling to Salt Lake City during school holidays, as you'll find a distinct lack of hotel rooms available, and much higher prices.