[TSM330i]

Rent a car and drive. You'll have fun in some of the areas where there is no speed limit. The autobahn is worth it, plus you can go off the beaten path to places the trains don't go.
Stay away from the very large cities (other than Munich) because they are typically just a large city and not much else. Just mostly industrial buildings etc.
Definitely make a stop at the Nurburgring. Rent a track prepped car if you can and have a blast (don't crash!). RSR is located 1 block from the track and a great bunch of guys.
Rothenburg is a fantastic old walled city and very pretty. I would say a definite must see.
Head South into the German Alps and go to Neuschwanstein. SO worth it!
Ulm is a nice city also with a good historical area.
Black Forest is great for driving too.

I've been to Germany five times for work and pleasure. Ein bier bitte!