East towards Vienna
1) Take the tramway #4 or #13 to direction Liebenau and get out at the station Murpark. There go back to the bus station along the motorway – there you can be seen from far distance and there is place to stop and go easy...Also there are a few gas stations along the way you go with the tram.
2) If you like it more to ask people at the petrol station directly you can go with the Tram number 6 from jakominiplatz to Schulzentrum St. Peter and from there you take the bus 72 to "messendorf heimgarten". wlak along the street 200m more and you find two gas stations. Loads of people go there to buy cheap gas because the highway is just a little bit farer along the street.
South towards Slovenia
Take the 32 bus south east to Trattfelderstraße. Just behind the stop is a bridge/overpass, with a ramp leading up. Carefully walk in the grass up to a traffic circle, where you'll see signs for any direction you want to go. There is a small shoulder right before the exit towards Slovenia, you can stand at the front of this area with your sign and get all the traffic heading towards Slovenia from this area.
Take the 52 bus heading north from Hauptbahnhof. After 10-15 min get off at the Shopping Nord on Wiener Strasse. This road leads into the E57 (=A9). there are many cars and places for drivers to pull over.
at the traffic light, it is really hard for people to stop. it is better to walk down the road until you find somewhere for people to pull in, though it is hard because people drive quickly.
Graz provides a tramway system, it is aligned star shaped around the center excange point Jakomini Platz. The tram and bus diagram can be found right here. The Tickets are bought directly in the Tram/Bus. A 1-hour ticket is € 1,90, a 1-day ticket is € 4,20 and the three day Tourist ticket comes to € 9,90.