By train
There is one direct Mugunghwa train per day from Seoul, which takes the better part of three hours to putter its way in. Other options are to take the Gyeongbu Line to Jochiwon and transfer there, or even taking the KTX to Daejeon and continuing from there.
By bus
Chungju's sparkling new bus station is located on the northern side of town in a big complex also housing a Lotte Mart hypermarket. There are hourly departures to Danyang 1:30, W6200.
By ship
In season, you can take a very scenic cruise across Chungju Lake to Danyang 2 hours, W18000, and you can go for a sightseeting spin on the lake throughout the year unless the lake freezes over entirely in winter. The ferry terminal is served by bus 301 30 minutes, W950, which leaves across the street from the bus terminal, but inquire at the tourist information office for schedules and whether the boats are running as there are only 9 buses a day.