Well, Aspen/Snowmass covers 4 out of 5 of your criteria, with the affordable accommodations being the tricky part.
You can access Aspen via their own airport ASE, which you can use public transportation (RFTA) from there to get around town and the different ski areas. Ajax and Highlands offer excellent on piste expert terrain, but I'm not sure if the Highland Bowl will be open by then. Snowmass has variety along with long bump runs at Camp Ground.
Otherwise, narrowing it down via close air transportation:
Aspen/Snowmass via ASE
Steamboat Springs via HDN - no car needed, especially if you stay mountain side. Lower elevation than other places in CO, unsure of conditions that time of the year.
Vail/BC via EGE - no car needed once in Avon or Vail, excellent public transportation.
Crested Butte via GUC - bus up to the town of Crested Butte, once there no car needed.
SLC - mulitple near by ski resorts (Alta, Snowbird, PCMR etc), unsure of public transportation though.
Breckenridge is higher up in Summit County, so you have a better chance at good conditions, the problem is its distance from the airports, either from DEN 2hrs or EGE 1.5hrs. You won't need a rental car once there, but getting there is the trick. CME runs shuttles from the airports, but those can get really expensive really fast.