I was in Stuttgart last summer. It isn't fabulous (and I think Frankfurt is definitely more interesting than Stuttgart), but there are a few things. The highlight for me was definitely the Mercedes-Benz museum -- definitely recommend it. It would take several hours to visit and isn't far on the S-bahn. There is also a Porsche museum but I didn't have time to visit it.

I did go to the state art museum (Stuttgart is the capital of whatever German state), which is reasonably interesting.