I'm from Germany and I used to live in Potsdam but moved to Victoria BC 2 years ago.
So of course my first tip is Potsdam. It's really nice City with lot of old castles and its' just 30min by train.
-Blind date with a different meaning http://www.dinner-in-the-dark.com/
-Potsdamer-Platz in Berlin http://www.bing.com/images/search?q=berlin+potsdamer+platz&FORM=BIFD
-If you have enough time and 60km is not far away then Tropical Islands is worth a trip http://en.wikipedia.org/wiki/Tropical_Islands it's huge artificial tropical resort in the world largest single hall without supporting pillars inside. It's a weired experience, its like biosphere on the moon.
-And don't miss the television tower http://en.wikipedia.org/wiki/Berlin_Fernsehturm The Space Needle has just the half of the height.
-Oh and if you wanna experience the Autobahn then rent a Porsche http://www.erento.net/rent/vehicles-boats-aircraft/special-cars/porsche/germany/ and go down the Berlin Ring to the A9 and have fun without speed limits. If you hit the 250km/h then there no need for coffee anymore.