Salt Lake City in the winter. 
Here you will find suggestions for activities in the area.
There are all sorts of fun activities you can do in the area, including, but not limited to, hiking, running, picnicing, road bicycling, mountain bicycling. I hope that as I have time I will post more information on good places to do these things. In the meantime, if you are interested, do a google search for your activity and "Salt Lake City". I am sure you will find some information there.