James' recommendations look like Budapest, which is also fun - esp. the baths. But, if you are staying in Vienna, we liked the Natural History Museum, dinner at Figlmuller - definitely make a reservation, Sandwiches for dinner and "the Torte" at the Sacher Café, and depending on interest, perhaps a performance by the Lippizanners. I took my daughter to just a practice session when she was 11, but have never seen a performance - I would say book early. We also took a tour by Fiakker at night and climbed to the top of the tower of St. Stephens. We found both the Hofburg and Schonnbrun very crowded between Christmas and New Years - to the point that I just had to get out of the buildings, but I like the Market at Schonnbrun and the walk up to the gloriette is fun. We also toured the Albertina, the Kunsthistoriche Museum and the Belvedere, but my kids are now college aged and older and opted to go see the new Star Wars film in VO on one day, and sleep in on another, so only joined us for the Albertina out of those three. They had quality sibling time, but were doing their own thing and didn't want to go to a museum every day...
While in Budapest, we all saw the Nutcracker and that is also an option in Vienna. The boys will perhaps say they don't want to go, as mine did, but they ended up liking it fairly well and I think everyone should see the ballet once - and doing it in Vienna or Budapest is just the best.