Courmayeur is a small village in Italy down of the Mt Blanc. Just behind the Mt. Blanc tunnel
The best spot is located, at a rotary at the end of the village. Just walk to the end of the main street of the village and you can see the sign where Courmayeur is about to end. Just stand on the barred area. The police came by twice and it was OK. You can also just show a sign with A 5, to get to the motorway which is going to Milan/Turin. From there it's easier to get a longer ride.
Walk the main street further. Leave Courmayeur and stand next to a gas station, ca. 5−10km down the street.
I got a ride from Chamonix through the tunnel. The driver dropped me off there and after 15 minutes wait I got my next ride to a gas station near the motorway, from where you can hitchhike easy to the main cities of Italy.