A front runner for Embark's "Most Entertaining Activity to Pronounce," Schlossplatz is Stuttgart's largest square, a hub of culture and society that always has something going on (festivals, concerts, markets, etc.) throughout the year. Surrounding the square is the epic Neues Schloss (New Castle), which is home to regional royalty; the Kunstmuseum (art museum), with pieces from Picasso to contemporary art; and other worthy attractions like the fountain, the statue of Concordia, and the Alte Schloss (Old Castle).
This historic square is close to anywhere in Stuttgart you'd want to go, so stop in and, at the very least, bask in the architecture and do a little people watching.
Note:For a great selection of restaurants, head west along Bolzstrasse or the pedestrian Königstrasse for traditional Swabian cuisine, a quick nibble of ice cream, or even a burrito.