Museum of Modern Art
This was my favorite museum that I went to in Vienna. I think I am just a huge fan of modern art in general, and this museum was AMAZING. They had such strange, creative exhibits, such as the "fat house" which was a house that you could go into, and the house was... fat. It looked almost like a cloud. Then when you went into it, there was a screen with the house talking in a sleepy voice, saying, "I am a house. I should not be inside. I am supposed to be outside."
That's just one example of the many strange, interesting exhibits they had - four floors of them! Oh, and a Red Hot Chili Peppers music video ("Can't Stop") was inspired by this very museum!