US tourists going to Munich area - tips?

We're looking at flying into München at the end of September and then traveling for 10 days around southern Germany, maybe into Austria and Switzerland. My wife and I both have ancestry from Black Forest area, Bavaria, and Switzerland.
I have a fascination for castles, and besides Neuschwanstein, what other great castles should we look at? We're not bier drinkers, so being there around Oktoberfest is really just a coincidence.

Vielen Dank für Ihre Hilfe!