I recommend taking this trip in December. While the weather may not be ideal the Christmas Markets are worth the trip. Markets are set up all over the city and include unique gifts and crafts, food, any my personal favorite thing about December, mulled wine.

Have a drink at the Das Loft bar in the Vienna Sofitel. This rooftop bar/restaurant offers sweeping views of the city and is an art installation itself. The ceiling was designed by multimedia artist, Pipilotti Rist.

Now, I did not get to do this activity myself, but I regret not doing it and wanted to pass on the wisdom. Viennese opera is world renowned and there are three main theaters in Vienna. You can go early the night of a show and pick up standing room tickets cheap. I linked to a helpful article here.