Thanks for all the info. I've decided to stay at the Motel One close to the Hauptbahnhof in large part because it looks like there's not much of anything to do (outside of the Mercedes museum) in the Neckarpark area.

Staying in central Stuttgart will give easy access to the Mercedes & Porsche museums, will be convenient for arriving and departing by train, and offer many more options for things to do and places to eat & drink. The Hilton Garden Inn looks like a nice hotel, and is part of the chain I'm loyal to, but not the best hotel if one is relying on public transport.

Now, if I just avoid the streets of Stuttgart between midnight and 3am I should be OK