Hauptbahnhof Central Station
It's in the Stuttgart train station. It was built in 1914-1927 with "neorealist" style under the direction of Paul Bonatz and EF Scholer. Its tower, which is 58 meters high, supports the Mercedes rotating star, which is the emblem of the city. I recommend you go upstairs, either by stairs or by elevator. The view of the city is breathtaking. Visiting is free every day except Monday, when it's closed. Inside the station you can take a tour and you can find out more information about prices and routes. Don't hesitate to ask the staff for help with something, they speak perfect English. You can get weekend deals, group rates, etc.