If you like orchestra, definitely see if you can get tickets to a performance at the Berlin Philharmonic. The building alone is worth it!
Similarly, if you are interested in seeing a match, if there's a Hertha Berlin home game on while you're there, it's worth going for the architecture alone (in the former Olympic Stadium where Jesse Owens ran in the Berlin Olympics)- even if there's no match on you can still visit the stadium.
My favourite museums are Pergamon (antiquities, including famous Babylonian lion gate), the DDR Museum (about life in East Germany), and the Deutsches Historitsches Museum (German history). I also love the new Ethnologisches Museum (anthropological museum). In general, I'm sure you've heard of Museum Insel which is a small island in the Spree with five museums, including the Pergamon. The others are the art gallery, the Altes Museum (Greek/Roman), Neues Museum (includes a lot of Egyptian artefacts including head of Nefertiti), and the Bode Museum (haven't been to this one but believe it's medieval).
If you like eating fun and casual local things you'll definitely want to try currywurst, which is sausage with curry powder and some other seasonings. Some places have vegan versions if you're not a meat eater.
Good luck with your planning!