Are you looking to stay in the mountains or do a day trip? pseudoswede's options seem better for a day trip. Good advice on the altitude acclimation though. Drink lots of water.
If you've never been to the area, most of the ski resorts are at least an hour and a half west of downtown Denver. Places like Aspen or Steamboat are closer to 4 hours. Mile High Stadium is right across the interstate from downtown.
If you are looking for a ski-resort type of experience, it may be difficult to redeem points for a property that is extremely convenient to the slopes. At Winter Park and Copper for example, the nearby properties are marketed by the ski resort and don't carry a Marriott or Hyatt flag. Vail has a Marriott property, and I believe Beaver Creek has some higher end stuff too, but those are quite a bit farther from Denver.
I'm partial to the beginner area at Winter Park, where I learned to ski at age 30. I've never participated in the Kids lessons, but the adult Never-Ever lessons were pretty good. If you land in the early evening Friday, I'd drive to Winter Park Friday night (stop at Beau Jo's in Idaho Springs for pizza) and stay the night there. Then Saturday afternoon after skiing, drive back to Denver and use points for your choice of property in downtown Denver. The full service Westin, Marriott, and Hyatts are all pretty comparable. The Sheraton is also fine, but a small step below the others IMO.
Enjoy the trip!