Canberra is the capital city of Australia.
Catch a bus that goes up Northbourne Ave to the intersection of Federal Hwy (route 23) and try to catch a ride going down Federal Hwy, which connects back on to the Hume Hwy (route 31) straight to Sydney. There is a nice stopping lane along the first kilometre or so of Federal Hwy, which makes it easy for cars to pull over, plus the speed limit is not very high at that stretch.
Also you can use this spot for heading South, if driver goes to Sydney, ask to drop you off just before Hume Hwy and then walk ~500 meters after left turn to find some spot
Catch a bus that goes up Northbourne Ave to the intersection of Barton Hwy (route 25) and try to catch a ride going up Barton Hwy, which connects back on to the Hume Hwy straight to Melbourne. Unfortunately, there is no good spot on Barton Hwy just after the intersection, the only option is to stay just after the intersection before 80 speed limit sign, but the traffic there is much lighter than on Federal Hwy, Oleg spent 30 minutes here with no success before changing spot to Federal Hwy. Alternately, you can get onto the Monaro Hwy (route 23) south of Canberra city, but this route will probably be more local traffic and less likely to find a ride straight through to Melbourne.