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To get to A38 road west in the direction of Paris, take bus #30 out of the town, pass the lake on your left and get out on a stop called Vaux Bruns. You'll see a wide road to your left with plenty of place for cars to stop.
In order to get to A31 we took Rue de Sully which is in the eastern part of Dijon right besides the Universite de Burgogne, Walk along the university buildings some 200 metres in the direction which leads out of the city towards east,there is a good spot for hitchhiking.
There is an on-ramp to the motorway A31 where almost all the cars go up the ramp heading towards Nancy, although some do also head south towards Lyon. To get there take bus #10 to the stop Boulevard de Chicago (right near the end of the route). Once you get off the bus, go that big intersection to your left, and follow the sign that says Toutes directions, and there you'll see where there is lots of room for cars to pull over near the traffic lights.
You can use the crossroad at Rue de Neuilly to get a lift to the first péage on the motorway which you want to use. To get there, take bus no. B12 in direction Chicago. Get off at Zipfel and you are right in front of the motorway ramp.
I had rather unfriendly experiences at this spot (August 2016). The lady of the petrol station where I stood, next to the crossroad, there told me and two fellow hitchers to leave immediately, this is private property, and how can we dare talking to her customers. The two people I talked to were unfriendly too and very much anti-hitch hikers. Directly after the petrol station is a place where cars can pull over too, that´s where the other two hitchers stood for already an hour before I arrived. I had to wait more than 1.5h to be picked up (direction Besancon) and the other girls were still waiting for a lift (=they waited for more than 2.5h). We all just wanted to get onto the motorway (A39) and didn´t succeed. The lady that picked me up was taking the country road into my direction, which was my salvation...
You should try to arrive at the péage of Dijon Sud. You can use that same crossroad at Rue de Neuilly and look for a lift towards Lyon or to the péage of Dijon Sud - see map (last time tried in March 2017 - one of the first cars stopped). You can also go directly to the péage by taking bus 15 to Perrigny, go down at the last stop, walk back a few meters, turn right to follow road D108 towards "Gare de triage de Gevrey", and continue straight towards the highway. That's about 2 km, 30 minutes.
There are many wine producers in the rural area between Dijon and Beaune. During the grape harvest (les vendanges) this area comes alive. For those participating in the harvest, looking for work there, or just wanting a rural day out in wine country, travelling between the villages on route D974 is easy and the locals are friendly and curious about hitchhikers and travellers. The D974 leaves Dijon from the south and you could start hitching anywhere along the Ave. Jean Jaurès where there are a number of places to pull in/out.
Of particular interest is the charming but somewhat bourgeois town of Nuits-St-Georges: D974 passes straight through the centre of this town, where there is particularly good dumpster diving, if you are low on supplies.