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Get yourself to the main road close to the city center. This road, ''Lakoba Street'' (ул. Лакоба), is where most foreigners have to obtain their visa (house #21). Walk southwards for about a kilometer few meters until you cross a bridge. Another 500m further is a sort of roundabout located with some shops and a stop for local mini busses. You can also take a minibus here, just stop them along the road. Just behind that bus stop it's a perfect spot to hitchhike southwards out of town. Try to get a ride at least towards the next GAI (police post), which is just a few kilometers further. Inbetween, the road is extremely narrow and people tend to drive very fast, it might be uncomfortable for the hitchhiker to stop cars there, though people might stop for you anyway.