We saw the usual tourist spots like Stephansdom cathedral and Hofburg Palace. Also Schönbrunn castle and the zoo was quite good. All the walking gives you a need for a break, and what is more obvious than the famous Café Central, with its beautiful ceiling.
Another day we had a river cruise, which was pleasant and gave us a lovely different view of the city from the water. Worth mentioning is also Ankeruhr at Hoher Markt. You will not find many alike even if you travel to a lot of other cities.
When you are at Schönbrunn castle, you must visit the gardens there. They are really worth a visit, and you can easily spend almost half a day there, be sure to visit the maze.
The Quieter Side
What I liked most were the smaller streets and hidden courtyards. Not much happens there, but they have their own quiet charm and you get a real sense of how people actually live in the city.
If you have the time, I recommend getting on a tour out of the city. We saw the beautiful Jagdschloss Mayerling and Heiligenkreuz Abbey. The abbey is still in function and lies in the woods southwest of Vienna.