Chungcheong is the central region of Korea, between the capital area and the southern provinces. Korea Trip Map covers two places here, and they are very different. Gongju was a capital of the ancient Baekje kingdom, and its hilltop fortress, royal tombs, museum and riverside temples are listed as World Heritage together with Buyeo and Iksan. Boryeong sits on the west coast, with the wide Daecheon Beach, the famous summer mud festival, islands reached by ferry and a long undersea tunnel.
Gongju is reachable from Seoul by KTX to a station outside town, followed by a short bus or taxi ride, or by express bus, in roughly an hour and a half to two hours. Boryeong is reachable by train to Daecheon Station or by express bus, in roughly two to three hours depending on traffic. The two are not close enough to combine easily without a car, so most visitors choose one. Check current timetables, because services change by season.
Plan around the season. Summer is the time for Boryeong's beaches and festival, when roads and accommodation fill quickly, while spring and autumn suit Gongju's fortress walls and leaf color. Other Chungcheong cities are not yet on this site. Opening hours, fares and conditions change, so check them before you travel.