Berlin -- probably my favorite city in the world! So much to do and see, and positively steeped in history! The food is excellent, the people are friendly, and the beer is world-class! Don't forget to take a walking tour, only 9 Euro with an ISIC card and well worth the money! After one day (and one night) here, you will never want to leave!
The Schöens Wochenende (Happy Weekend) train ticket is an amazing deal if you have more time than money. For only €28 up to five people can travel all weekend on local trains (that's €28 total for up to 5 people!). If you wanted to, you can travel all the way from Berlin to Switzerland on nothing but local trains (but it takes about 10 train transfers and 10 hours to do it). Buy a pass at any German train station.
I suggest also going to the DDR Museum -- it's very different than all the other museums, with the exhibits being largely hands on and showing what life was like growing up in the DDR. It's by the river on the Alexanderplatz side of the Berliner Dom.
The Schönes-Wochenende-Ticket is now thirty euro, and is only good for one day (on either Saturday or Sunday). It is still good for up to five people and still only for local transport. Döner kebab and curry-wurst were both invented in Berlin, so try them both!
If you go to East Berlin, you have to consider that the East (and West also) had been isolated for fifty years and old people still have the cold war inside their brains. Go to district of Kreuzberg and Neukölln -- Germans are the minority there, or go to Vienna.
If you do nothing else in Berlin, make sure you book onto a walking tour. They cost about $12 and in just four hours you have a guide take you to all the main sites around the city. Well worth the money!
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