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When approaching Yatağan from west (Milas, Bodrum), try to get a direct lift directly to the town centre. Some drivers who are driving to the big power plant 4 km west of Yatağan take hitchhikers without exactly informing about their destination (i.e. just saying that they are driving to Yatağan), and it's almost impossible to get a lift from the power plant to the town centre. So you may have to walk that last 4-km section (which has a bit of an uphill section) under a cruel sun!
Highway coming from north (Aydın) and heading south (D550) passes about 2 km east of the town centre, so you have no other option but to walk there. Once at the junction, with the help of the traffic lights and the large shoulder there, you can get a fairly quick lift — in fact this is one of the places where you can get quickest lifts in all of Muğla (Province).
Places to avoid
At the western entrance of the town (on the highway from Milas, Bodrum, and the power plant), there are two gas stations side by side. The first one is M-Oil, and the employees there are very unfriendly, presumably because of the "hotel" there, which likely is an unofficial brothel (think of dodgy stairs at the back of the station into somewhere signed — but in no way advertised with big sings at the front — as "hotel"), and thence the need to "hide" it. Try to avoid this station, no matter what you are looking for - toilet, telephone or a shop (and unfortunately they have all, but still staff follows you all around and asks what you are doing there all the time). The second one, Shell, which is nearer to the town, has far friendlier staff and there are toilets and a shop there too — and a nice gazebo at the side of their garden where you can rest, or may be have an ice-cream you just bought from the shop.
Another thing to avoid while in Yatağan is to overnight with a tent in the vicinity. The coal-burning power plant sometimes —and nobody knows exactly when but almost always during night— unlawfully discharges smoke from its chimney, and sometimes the pollution gets to lethal levels, insomuch as that a curfew is levied in the town. Plan ahead carefully as not to get stuck in Yatağan through the night so that you don't have to camp.