Sivas is actually an ideal city for hitchhiking out of. One spot serves all directions. On the southern edge of the city is a big roundabout where the E88 passes by the city, and intersects the D850 road. It's also right next to the central Otogar (bus station) in the unlikely event that you have trouble finding a ride.
If you're heading south, stay on the roundabout level, and at the end of the roundabout you can hitch a ride easily towards Malatya or Elbistan. To go any other direction, simply walk up the on-ramp in the direction of your choice and start thumbing a ride from there.
Walking from this location to the centre of the city takes around 25-30 minutes.