The Futurium is a quite cool new Museum. Located close to the Hauptbahnhof (Berlin Main Station). Its for free. Its a Museum about the future with lots of interesting stuff on for example future of medicine, future of transport and so on. It has a positive view on many topics even though it of course adresses also the problems. Just super cool and very interactive.
Most of the Museums are free for people younger than 18 anyways. But for adults the Museum pass is a great advice.