I don't think Berlin has the 'typically German' feel you're looking for. The following is very touristy, but that's what we are, right? Travel over to Rothenburg ob der Tauber, spend a night, then down the Romantic Road to Munich. I'm prejudiced, as I lived there for 2 years, but think Munich is the greatest town in Germany. So much to see & do, no matter what your interests. (BTW, let us know them & we can make suggestions...) It's a beautiful city & you won't be bored. Can do a day trip to the Alps or Schloß Neuschwanstein from there, too.