How can you not venture into this "obvious" and strange building! If it's winter, there's a great (but not cheap) cafe. There's an interesting (but not cheap) gift shop. . . and the museum itself-- well, not cheap, but if you have the time and are in the mood for modern and contemporary art, go for it!
If you own or manage Kunsthaus Graz, register now for free tools to enhance your listing, attract new reviews, and respond to reviewers.