Between the 3 castles (Potsdam and Charlottenburg in Berlin and the one in Vienna) I would pick just one and go there (probably the one in Vienna). With so little time you have if you go for more than one they'll get mixed in your head anyway.
When in Prague try to meet Karel
I double Andrey's advice to go to the black theatre. It's great fun. On the other hand do not go to any concerts in the churches in Vienna- the price is high and the musicians are mediocre at the best.
The museums in Berlin - see what interests you and go only to the things that do. Pergamon is rather big, but perhaps you don't care about all that is there. The arts museum is rather small and very nice, there are some lovely paintings. I would skip the audio guide there (though it's free if am not mistaken) - it takes you to too many not particularly interesting paintings.
In Vienna don't go to EVERY place realted to Sisi - at some point you might be in a Sisi overdose and feel that if you see another plate or dress you'll jump off something.
Check which concerts go on there (both classical and not - many interesting artists perform well, at least in Berlin)