Other people will probably tell you about the sites. I like food, so I’ll recommend some restaurants I like.
Uncle is a (pretty trendy) noodle house in the Highland neighborhood. No reservations, so get there early. The fried green tomato steamed buns are outstanding, as are the ramen bowls.
Domo serves traditional Northern Japanese dishes. A former co-worker from Hokkaido told me it was the closest he’s ever had to his native cuisine in the US. Very cool building, though the neighborhood is a little industrial.
Duo, also in the trendy Highland area, is really good. Not inexpensive, but the food is interesting and really well made.
Masalaa, in Aurora, is a South Indian, vegetarian restaurant that is insanely good and cheap. It’s in a tiny strip mall in an area with zero character, but it’s totally worth finding.
Colorado is paradise for craft beer lovers. There are now something like 250 craft breweries in the state, and a lot of them are in the Denver-Boulder-Fort Collins area. I mostly know the breweries in Boulder. If you’re into that, I can provide a list. The New Belgium Brewery in Fort Collins (makers of Fat Tire) has brewery tours, and it’s probably only about an hour drive from Denver. Craft distilling is also getting big. Denver has Stranahan’s whiskey distillery. Boulder has several interesting places. Again, I’ll provide a list if you’re into drinking. Do note that you shouldn’t drink a lot your first couple of days at this altitude. It won’t take much to get you tipsy. (Also, drink a lot of water when you first arrive. It’s really, really dry. Water will stave off altitude headaches.)
Drive up to the mountains for spectacular scenery. Rocky Mountain National Park is about 90 minutes from Denver, though it might be getting a bit chilly, and I think Trail Ridge Road may be closed already.
Come to Boulder and walk around the Pearl Street Mall (if you do that, make sure to get truffles at Piece, Love, and Chocolate a few blocks west of the pedestrian mall) and hike in Chautauqua Park up to the Flatirons, or go to the I. M. Pei designed NCAR Mesa Lab for fantastic views and a small, but well done, science museum.
Have fun!