I'm surprised more people haven't mentioned traveling along the Rhine. There are so many things to see there:
- Bonn to see where Beethoven was born, if you're into that
- All of the wineries. You can find Spatburgunder, Riesling obviously and many other varietals depending on the area. If you get there around harvest time (usually around September), you'll find a lot of festivals in the little towns that dot the Rhine. It's a great time.
- Small town culture. It's really relaxing, the people are great, and you'll find a lot of history. Most of the little towns have a long history during the feudal times, wars, etc. Many have castles above the hills that you can visit.
I would also recommend Munich, especially since it's not that far to get to the Rhine. Cologne is a very nice city as well, and the cathedral would definitely be something to see even if it is a tourist trap.
Finally, Rothenburg is a great time. It's a walled medieval city, and while I wouldn't vacation there for a long time, it is worth a visit.
So, that's what I'd do. All of Germany is wonderful, in my opinion, but you have a lot more options in the west/southwest. You could even go further south to see Neuschwanstein, the Swiss Alps, Austria (Salzburg isn't that far from there), etc.
Ich liebe Deutschland.