I know exactly where that is...

Have fun.
If you want - I know a really neat restaurant in the old (as in VERY old) section of town. Had an awesome dinner there. Can send you the name of that place if wanted.
OK - nevermind. I'll let everyone know...
Zum Ackerburger (google maps) or
Homepage
Parking is a challenge... but doable (at least the two times I was there, I found something kinda close)
I see now that Tripadvisor has it as #4 out of ... a thousand or so restaurants in Stuttgart.
There are LOTS of places that were fun there.
Cheers!