Esso gas station Heilbronnerstr: From Hauptbahnhof (Central Station) take Metro U5/U6/U7 just one stop to "Türlenstr./Bürgerhospital". Leave the station in driving direction and walk about 100m up the hill. On the right side there is the gas station where many people fill there tanks before they're entering the motorway.
From Hauptbahnhof (Central Station) take Metro 15/U5 to "Borsigstr.". When you leave the train, there is one gas station in front of you (direction of the train) and one gas station behind you. The gas station behind you is a better spot to hitchhike because the cars have a better opportunity to stop and the gas station is a little bit bigger than the other one. Most of the cars that stop there go on the highway ("Autobahn") A 81. In average I needed about 15 minutes to get a ride (on weekends).
When you are on highway (Autobahn) A 81 you can jump off on the resting place called "Wunnenstein" that has also a petrol station and is between Stuttgart and Heilbronn or rather the departure to highway (Autobahn) A 6. From there you can get rides to the north or west. But there I sometimes had to wait longer (about 45 minutes in average) to get a ride to the north because a lot of cars are going to the west.