If in Stuttgart, be sure to visit the museum from Porsche's cross-town neighbors too! The Mercedes museum is an awesome history of a company that has spanned the history of the internal combustion engine. About an hour south of Stuttgart (on the way toward Munich) is Hohenzollern castle near Balingen.
It is the ancestral home of the Hohenzollern family which became the Kaisers of Germany. They never actually lived there much, but did turn it into a a very fascinating museum. There is a great armory there full of medieval armor. The Kaiser side of the family was Protestant, but there was another Catholic branch ( Hohenzollern-Sigmaringen ) who set up their home in a real castle in the nearby town of Sigmaringen.
In that castle you can see how the royalty really lived, and find out how a German came to be Emperor of Mexico.
Things to do in Munich??? My personal favorite is to go to the Alps and just go for a walk or a drive. Just head south into the mountains and explore. In Munich you should check out the BMW Museum. I'm not sure if Audi has a museum, but if they do it's most likely in Inglestadt which is just a little bit north of Munich. If you are into history, I'd recommend visiting Dachau -- it will be very moving. It's located near Inglestadt.
Salzburg is also only about 90 minutes(?) east of Munich and very pleasant to visit. It's a much prettier city then Munich. To be honest there is at least a weekend's worth of things to do in Salzburg -- especially if you like The Sound of Music.
Southwest of Munich is Neuschwanstein (Germany's most famous castle, it was used in Chitty-Chitty-Bang-Bang and was the inspiration for the Disney castle) which is very, very scenic.
It's not a "real" castle, but it's awfully impressive none the less. The tour guide will explain why when you're there. Just walking distance away from Neuschwanstein is a real castle (palace actually) of Hohenschwangau which was one of the family homes of the Bavarian royal family. You could take a full day on just those two places. Beware of lines on nice days though.
No matter where you are, ask about any local beer-fests or wine-fests. They are held all summer. Each town has one, it's just a question of finding out which town has it the weekends that you are there. The food is cheap, the beer and wine will be plentiful and the music and fun are free. It's kind of like the Octoberfest, but smaller and less crowded.