A general favorite is the Amadeus just close to the Old Schloss in the city center. However, there are so many other places to go. Check the Stuttgart Web pages or get a recent issue of the Prince magazine of Stuttgart. Here you will find what the 'inthings'in the city.
In the suburbs you find brooms hanging out at regular homes during certain times of the year. Here are the places where the locals come together and drinking wine. It is not a sign of a pub but just a colourfull broom as an invitation. Prices are really affordable for the budget tourist in those places.
Stuttgart is also home of the second largest fair beside the Oktoberfest inthe world- the Cannstatter Wasen which takes place in late September.