there are many things to do at Stuttgart (don't hesitate to ask questions, I did grow up in Stuttgart area)

a) you may want to consider one of the worlds best ballets
b) you already mentionned the Porsche and Mercedes Museum
c) there are some nice SPAs
d) the television tower (the modell for all television towers worldwide)

some nice castles nearby, I'd say there is definitely no need for a car. A day trip to Heidelberg would be a nice add-on (40min by train, 1h30 by car )

What about a visit at the Technikmuseum in Sinsheim / Speyer?
The museum has the Tupolev and the Concorde and especially for kids it ist very interesting.
so in what mood are you? I'll try to answer all your questions here

have a look at the following threads as well:
http://www.flyertalk.com/forum/showt...ight=stuttgart
http://www.flyertalk.com/forum/showt...ight=stuttgart

and you'll have no problems with english