There are million and one things to do in Stuttgart. It is recommended to start at the Tourist Office outside of the Stuttgart Hauptbahnhof and then spend at least half a day walking down Koenigstrasse. Stop at an outdoor cafe, or enjoy some ice cream in summer, or put on your ice skates in winter. There is lots of shopping and site seeing in a one mile radius of the Stuttgart Hauptbahnhof.
Outside of Stuttgart there are many small villages that were untouched by the bombings of WWII. Many of these small villages hold thier own treasures for the traveler. You can tour the castle at Ludwigsburg, or watch a bird-of-prey show in Bad Wimpfen. And who would miss out on the Medieval Christmas festival in Esslingen. Instead of spending all of your travel time in the city, take a tour into the beautiful southern German country side.