I have been traveling around Europe with my girlfriend and we spent 1 week in Vienna. As everyone else has mentioned, the apartment really is in the best location. Not only is it half a block from the opera, Kartner Strasse and the Sacher Hotel but it was easy to get to from the train station and easy to get from, to the airport which is what we did. The U-bahn from Karlsplatz will get you anywhere in a matter of minutes.
The apartment was more of a studio with the bedroom being more of a nook than a room - but it was comfortable and clean. We found the large number and size of paintings somewhat overwhelming for the small bedroom. Our only issue was with the hot water. The shower would either be scalding hot or freezing cold and wouldn't settle in the middle. Even the slightest movement of the tap would push the temperature to one of its extremes. We called the people who are looking after the apartment who came out and claimed it was a very 'intelligent' system and explained how to use it properly. They also offered to have the system looked at if it still didn't work. Unfortunately the system didn't get any better but we decided not to take up their offer, in order to not disrupt our holiday. I do, however, suggest that the owners have it looked at before their next guests arrive. Overall though, it was a great place to stay and we would stay here again. We highly recommend this apartment.