Mersin is a city in southern Turkey, on the Mediterranean coast.
Hitching out
West to Erdemli, Silifke, Taşucu (and ultimately Antalya)
Get on the white minibusses (called Mes-koop) and get of at "TED Koleji", which is also end of the highway.
East to Tarsus, Adana
The traffic between Mersin and Adana is full with local traffic, it can be hard to get a ride but the train to Adana is real cheap (something like 3 TL for a one-way trip), frequent, and comfortable, so better to go Adana by train and hitchhike from there. To avoid suburban sprawl east of Adana, you can take cheap trains further east to Osmaniye or İslahiye.