You are in luck because there is actually a museum dedicated to Bauhaus! It's called the Bauhaus Archive!
Another amazing option is the contemporary art museum, Hamburger Bahnhof, which is worth a trip just to see the building! It's inside the old Berlin-Hamburg Railway terminal.
This might not be exactly what you're looking for, but something that you absolutely cannot miss when in Berlin is the East Side Gallery (Berlin). It's a national memorial and one of the best art installations in Berlin. It's a 1.3km stretch of the original Berlin Wall that is now covered in murals.
This isn't art related, but it is a museum that you shouldn't miss. Topography of Terror, which is a Germany history museum located on the grounds where the Gestapo were headquartered during the Nazi regime.
I second the recommendation for the Old National Gallery museum, but the good news is that Museum Island has a number of museums to choose from. So based on your tastes, you can choose the most appropriate one. BTW, I would visit Alte Pinakothek while you are in Munich as well. :-)
This is not a usual museum but if you have time and if you are interested in art, you must for sure visit the East Side Gallery. It is a piece of the wall where artist have made into a art manifestation it is a great and different and truly catches the essence of Berlin.
We really loved the Old National Gallery (Alte Nationalgalerie) but it's definitely a romantic and impressionist collection.