I spent a month in Berlin back in 1965 when I was 15 and studying German. I then went back 40 years later in 2005 with my youngest daughter who was about to take public exams in German too - a very different place, following the removal of The Wall.
If you do get to Berlin, buy yourself a Tageskarte - a daily ticket which gives you unrestricted travel on buses, trams, the U-Bahn, and the S-Bahn. Getting around the city by public transport is very easy and it works brilliantly, in true German fashion.
In no particular order, try to see (a good guidebook will expand):-
The Brandenburg Gate
The Deutsches Museum
The Kurfurstendamm (Ku'dam) - one of Berlin's most important streets
The Kaiser Wilhelm Gedachtniskirche
KaDeWe (Kaufhaus des Westens) - huge department store
Checkpoint Charlie - nothing like as bleak as it was when I saw it in 1965. Some remains of The Wall can be found nearby.
Being Jewish, I was also keen to see
The Jewish Museum - Daniel Liebeskind's architecture is stunning
The Holocaust Memorial - very simple, but very effective, memorial next to the Brandenburg Gate
Can't remember any more. Have fun!