Munich and Cologne are probably my two favorite cities in Germany. Cologne has a lot of history and while it was heavily bombed in WWII there's still lovely architecture in the Old Town to be seen. Munich has great attractions too like the Salzburg Nuremburg and the Neuschwanstein castle. anyone visited Munich or Cologne? what's your favorite place in Germany?
You can easily visit both cities by hopping on the ICE (fast train) which takes 4½ hours either way and costs around €113 ($150). There is also the bus option: ADAC Postbus which is cheap (30 €) but takes nearly 9 hours.
if you base yourself in Berlin, you can always rent a car and drive West to the Rhine region and see Bonn/Cologne, but also tour the Rhine Valley. You will find quaint villages and many great castles along the Rhine. It may not be Rothenburg or Neuschwanstein, but I am certain you will enjoy it and you will be able to nestle into your trip much more comfortably.