Europeans currently fly all over their continent for weekends in Barcelona, Berlin, Belgrade, you name it. Join them. There is plenty of good advice on Berlin on this site and in Rick's new series and guidebook. My personal memories of Berlin from before the Wall came down are still vivid. Include the Museum Island to see great historical art, the National Gallery (designed by Mies van Der Rohe) to see the building and the work of Ernst Barlach, a master sculptor of faces and figures. and the graphics by Kaethe Kollwiitz. Make time for a bus tour to get an overview, and try to imagine Berlin when Checkpoint Charlie was not just a small US hut and barrier, but a vast concrete holding pen that everyone entering or leaving East Berlin had to submit to. Watch Spielberg's Bridge of Spies before you go to get that feeling of oppression.. A teenager spat at me and called me a spy when I walked past him, the same age, in 1969.
A walking tour with a student guide your age would be money well spent. Dress warmly and enjoy Europe's newest old capital. Just watch out for the raised cobblestones marked with the names of Berliners arrested and sent to their deaths by the Nazis. Remember.