London: Can't leave Europe without doing… ?
Berlin - Take a walking tour from Hackescher Marktto get some history from a usually entertaining host. Visit the Holocaust Memorial, Museum Island, take a boat cruise along the spree to take in the architekture....
Berlin: Music scene in Berlin
Electronic music, particularly dance music is Berlin's penchant. Berghain (the techno mecca) - best to sleep then go sunday morning super early and stay for the day/evening. It's much less touristy and you can usually catch some big dj sorts playing in Berghain...