Stuttgart Airport (www.flughafen-stuttgart.de) is located approximately 13 km from the center. With the S-Bahn (rapid transit system) lines S2 and S3 it will take you 27 minutes to the central station, without changing trains. The S-Bahn runs from about 5 a.m. til midnight, every 10 to 20 minutes. Warning: On weekends you sometimes have to wait 30 minutes for the next train - it also only starts at 5.30 a.m.  Also, several buses stop at the airport. A public transport VVS ticket costs 2,- euros (valid for two hours when moving into the same direction). Of course you can also take a taxi, with the Hoffmann shuttle service the fare for 4 people is between 20,- and 30,-  euros. On the company's  website you can calculate the price in advance. (http://www.flughafen-shuttle-stuttgart.de)