Let me try it

I would cross out:
Dortmund, Erfurt, Essen, Freiburg, Goettingen, Hannover, Kassel, Mannheim.

Typical must sees are:
Cologne, Dresden, Hamburg, Munich

Fantastic hidden gems are:
Nuremberg, Würzburg

Special interest might be:
Bonn, Dusseldorf, Leipzig, Stuttgart

All of these are in two to five hours train distance or cheap (50 to 100 Euro) flight disteance to Berlin