There are plenty of VRBO units in Breckenridge, I would honestly go that direction. Then you can get groceries and not have to worry about trying to find places to eat when it's freezing cold.
Alternatively, I recommend Winter Park. Also a lot of VRBO areas (both in town and in Fraser, which is the next town, and really all one), and you can do snowmobile tours up on the Continental Divide, and sled dog tours in town. There's a skating rink in the resort center, several different tubing hills, and great lessons for skiing/snowboarding if you want to try it. It's also a bit more off the beaten path, and would be a lot less crowded than Breckenridge and the rest of Summit County.