General:
1) Denver is fun city. Downtown and Lodo for culture, food and fun. Cherry Creek for shopping.
2) See the Mountains for a day or two. You can drive up or take a bus if you don't like winter driving.
3) Boulder and Colorado Springs are excellent non-mountian day trips, too.
Specifics:
Best History: Our History Museum is closed for rebuilding. So State Capitol and Buffalo Bill Museum if you are into history.
Best Art: Denver Art Museum is terrific, and the Kirlkand Museum is cool too.
Best for Kids: Zoo, Skiing/Snowboarding, Museum of Nature and Science, stadium tours, Aquarium
Sports: Avs and Nuggest at Pepsi Center. Pepsi Center, Coors Field and Invesco Field all have public tours.
Best Food: Denver has good steaks, good mexican and some high end restaurants in downtown, Cherry Creek and Lodo.
Adult Fun : Coors Brewery Tour