Well the only place I've been in Austria around that time of year is Vienna & I would recommend it, if you ski you might have different ideas. They have Xmas markets right up until the New Year and the decorations are beautiful & there is a lovely atmosphere. From Vienna you could also do a day trip to Budapest (or Salzburg) & visit the Xmas markets there or in a town outside Vienna. Alternatively you could base yourself in Salzburg which has a castle and is famous for its Sound of Music attractions. It is also a beautiful city.
Link for trips
Try and take in a concert or two at Schonbrunn Palace for example & the Vienna Boys Choir. Even if you're not into churches the one at Melk is stunning. I stayed in the 4^ historic hotel, Hotel Stefanie.
Please also view this link & do a search for Vienna here.
http://answers.worldnomads.com/questions/austria/5351/in-vienna-for-3-days-what-are-must-see-places about 7 years ago