These are a few links to information about:
Berlin Museums Info
A must see museum is the Pergamon. It opens at 10 am, but you need to get there early as the queue for the entrance tickets gets very long and very quick.
State museums grant free admission on Thursdays for four hours before closing. For further Information take a look at their website, click the English version, www.smb.museum.
The museum of the Allied Forces (American, British and French Allies only) in Berlin, the Outpost (a former cinema for American soldiers) gives you a profound insight of Berlin history from 1945 until the reunification of Berlin. Admission is FREE. The location is a bit off the main tourist track, but easy to reach by public transport. www.alliiertenmuseum.de
The Deutsche Bank & the Salomon R. Guggenheim museum offers modern art for FREE each Monday in the center of Berlin, Unter den Linden 13. www.deutsche-guggenheim-berlin.de
Palaces & Gardens around Berlin