If you are interested in Aspen as an option I would check out their
Central Reservations website...they have a booking engine that
publishes most of their inventory. If you can't find it online, their
vacation specialists usually have the "inside scoop" on what you are
looking for.

http://www.stayaspensnowmass.com

They have access to almost 100% of the lodging base in Aspen and
Snowmass. Often, you can find ski in/ski out condos in Snowmass the
first week in January for around your desired price range.

Also, having skiied both Vail and Aspen's Mountains I would say that if
you want to stay away from the crowds definitely go to Aspen.