There are private condos for rent and a Ritz Carlton Destination Club on the mountain but the primary local option is to stay in the Town of Aspen Colorado which is a great option given that Aspen has 100's of restaurants, plenty of shopping and lots of places to stay and is a beautiful town in any season.
Ritz Carlton Destination Club condos (membership required)
Hotel Jerome: downtown Aspen
Aspen Mountain Lodge on Main St (walking distance to downtown or take the bus)