Here's a few.
For Berlin, Unsere Mütter, Unsere Väter, A Woman in Berlin (both of these are a little hard to watch at times), Der Tunnel (if you can find it), The Lives of Others, Goodbye Lenin, and because not every movie set in Germany has to be about Nazis or Communists, Run, Lola, Run.
For Prague, Kolya.
The only movie I can think of set in Munich that might be available in the US is The Last Days of Sophie Scholl, but most of the film takes place in court rooms and Gestapo offices. You see very little of the actual city.
For Austria/Bavaria, the series of Sissi films from the 50s starring Romy Schneider have remained extremely popular throughout the years, although they're not too well known in the US.