Definitely do Red Rocks since it is just on the west end of town (just a couple miles from my house, actually...). The hikes in that area are pretty easy, plus Red Rocks itself is great and free (when there's no concert going on...) so you can even walk around the seating area. Here's their website for more info:
Welcome to Red Rocks
Driving conditions are a little slicker in the Red Rocks area of town - but that's really only when it snows. Usually they keep the roads pretty clean and it's an easy drive unless it's actually snowing, since it's hard to keep up with the current snowfall. Just take it slow and steady if it does snow.
Also near Red Rocks is a place called Dinosaur Ridge:
Search this site
It's right on the other side of the "hog back" from Red Rocks - which is a small mountain/hill that runs all along the west side of town. It's a museum dedicated to the dino fossils in that area, and the small road that goes up and over the hog back from the museum to Red Rocks has some places where you can pull off and look at the fossils right there in the rock faces - pretty cool.
I second the Lookout Mountain/Golden (on the same side of town/within 5 miles of Red Rocks), 16th St Mall in downtown Denver, and Pearl Street up in Boulder. Since it's winter and a little cold, there probably won't be as many buskers and colorful people on the two malls, but it's still fun to walk around. If you are at all into the "hippie" side of things, definitely do Pearl Street, and also "The Hill" in Boulder - a great area with lots of "hippie" stores/people.
Jason