Yeosu (여수) is a city in South Korea.
North towards Suncheon
Use a Korean navigation app (Naver Maps is very good and available in English) to find a bus (or walk, if staying near the EXPO site) to the city's train station, Yeosu EXPO Station. National road 17 runs North/South along the train station and is the major road out of Yeosu. There's a long turning lane on the road's Northbound portion that's a good spot for cars to stop and pick you up, simply stand on the side of the road and put up your thumb. Very few cars use the turn-off on the right hand side of the tunnel, and almost all cars entering the tunnel here have their destination near Suncheon or one of the nearby towns, from where you can proceed further. Ask to get dropped off at one of the toll gates if your destination is further afield (ie Gwangju, Busan).