I have always been a fan of Mozart. They turned a house that he lived in Vienna into a museum. It was nice, but I really wish they have mapped out his works overtime. At the Van Gogh museum, they show how he changed overtime.
The museum covers a brief history of Mozart. It shows where he lived but unfortunately, there was really any of his belongings. They did include an audio guide that allowed you to listen some of the operas he wrote and letters that were written to/from him.
If you have not seen the 1984 Amadeus movie, I highly recommend that you do. It is not entirely accurate, but it is still a wonderful film. The soundtrack is amazing.