The first time I was in Vienna 5 years ago, I realized that it was my city. And now by the will of fate I have been living in the capital of Austria for a year and I can confidently advise others: a tour of Vienna is certainly good, but if you want to feel this city for real, do the following yourself:
1. Walk around the center
But don't spend more than two days on this - if you have time left, spend it getting to know the city from a different, non-tourist side. The Inner City (Innere Stadt) is quite compact. All the sights in Vienna can be seen on foot: the Opera House, the Parliament, the Rathaus, the Natural History Museum and so on. All this information is in any guidebook. But few people know about other highlights of the city.