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However I tried starting from inside the city a few times (between Moskva ter and Kelenföld), but I never got a lift, although there was a lot of traffic (really much) in my direction, and the place was good for stopping. So I have no clue, why don't want to pick up someone inside the city.
There's a good point inside Budapest also. It's in the above metioned mentioned neighborhood Kelenföld, on the Budaörsi út (road). You can check the schedule on the homepage [http://www.bkv.hu/angol/home/index.html] of the local transport company, but the bus number 40, 41, 53, 139, 153 are ok. You should try on the ÖMW OMV petrol station.
An other option to get to this petrol station is to take the tram 19 or 49, go to the last stop (it's in the front of small train station), then walk along the train station until the walking tunnel, go to the right inside the tunnel, on the exit walk straight until you see the highway, then go to right and cross the road by the walking bridge, go to left and walk in direction of the mcdonald (where the petrol station is).
The best is to use a sign "M1" or "M7", according if you want go to west or to south.
There is also another petrol station just ~5km further directly before the fork of the highway to M1 or M7. But it seems that you'll find less cars here than at the ÖMV OMV petrol station. There is another OMV petrol station which is even closer to the city center. It is situated at the beginning of Budaörsi út. You can reach it easily by taking tram no.61 from Moszkva Ter. Coming from Pest side you should take bus no.112. There is a lot of traffic to M1 and M7. It took us 20min to get a lift to Tatabanya. Our Hungarian friend told us that he never has to wait more than 30min.
===M5 South towards [[Belgrade]], [[Arad]] ===