If you are classical music buffs, I would also suggest the opera. A tour of the opera is also very interesting. They also offer tours of the Musikverein (where the Philharmonic plays.) I have never taken this one, but I'm sure it is interesting as well. You will be approached by many "Mozarts" trying to get you to go to their concerts - they are ok, but I would stick to the "real" concerts.

Other interesting sites are the two palaces - the Hofburg and Schoenbrun. You should spend an afternoon at a coffee house - Demel is my favorite, but you should also visit the Sacher Hotel for an "original" piece of Sacher Torte.

December will most likely be cloudy and cold, but not unbearable.

Vienna is a wonderful city, and you will have a blast! Let me know if you have any other questions, or need any additional recommendations.

Josh