These are a few links to information about:

Berlin Museums Info

 The museums in Berlin tend to be clustered around a few key areas, which include the museum usland, postdamer platz, and around Dahlem. The further you go, the more interesting and less classical the museums become. The Museumminstel is good for archeology, and some pre-20th century art, as well as the main history museum. Right above the island is the main contemporary art museu. Postdamer platz includes the main modern art place, with the New National Galley, and Culture Center. There's also the main old european art museum. Further down are perhaps the most unexpected museums, which include the excellent museum of ethnography, Asian Art, and Western culture. These museums are tightly interwoven, and often host very thought provoking exhibitions.

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,

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.

The Deutsche Bank & the Salomon R. Guggenheim museum offers modern art for FREE each Monday in the center of  Berlin, Unter den Linden 13.

Palaces & Gardens around Berlin

Berlin Sights - Sightseeing Info