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Muğla is a city in (and, indeed, the capital of) Muğla Province, southwestern Turkey. Although Muğla Province is well-known for its sea-side resorts, Muğla lies on the upland section of the province, away from the sea. It lies on the highway that heads south to famous resort towns.
It's best to let your driver drop you off at the ring road that partially surrounds the city if coming from north with no intention of visiting the city of Muğla itself. To the south of the town, there is a junction where the road from the city centre and the ring road that carries long-distance traffic intersects. This likely is the best spot around as you don't miss southbound traffic from any direction. And there are traffic lights at the junction which lets traffic from each direction once at a time, so no drivers can pass by without seeing you. Large shoulder helps as well.
It takes around half an hour to attract a lift here.