The KTX from Seoul takes just 35-40 (depending on which train) minutes to zip to Cheonan-Asan Station (W12800), but you'll need to connect to the painfully slow #20 or #13 bus (W1200 without a card) to get to central the Shingsegae/Bus Terminal area of Cheonan. Alternatively, you can walk about 200m to Asan Station, where for W1000 you can get a 5 minute subway (not underground) train ride into Cheonan Station. From here you can connect to both north lines going towards Suwon/Seoul or to the south lines heading to either Busan or Gwangju/Mokpo.
Alternatively, you can take a 급행 (express) subway directly to Seoul or Yongsan stations in about an hour and a half. These trains run roughly once per hour. You can find the up-to-date timetables in the ticketing area of Cheonan station where you enter for the subway only lines.
The express and intercity bus terminals are located near each other in the northern part of town. Note that the intercity terminal is hidden in the basement of the Galleria shopping mall.
A complex and confusing system of buses covers the area, but there is no information whatsoever in English at the stops or in the buses themselves. However, nearly all services start from or terminate at the intercity bus terminal.
The subway line has been extended from Cheonan Station to KTX Cheonan-Asan station and continuing to Asan.
Gagwonsa Buddhist temple at Taejosan (Mt. Taejo) 태조산 A nice place to go hiking. The Buddhist temple has one of the largest sitting Buddhas in Asia/Korea or something like that...
Upstairs from the bus station is a movie theater which plays korean and western films.
Mount Fishtail, Cheonan Station (천안 역) Probably the only South-Asian curry restaurant in Cheonan. Decently priced curries (to be Korea), around 8000-10000 won per dish. Owned by a lovely Nepalese couple. It's right across the road from the taxi stands by the station, right hand side, second floor.
Banana Bar in Shinbudong, across the road from Ya Woo Ri shopping mall is a great place to meet people. Pool competitions; open mic night; quiz night; full stage for performers and bands. 010-3424-6309 Speak to Mr Oh, he's very friendly.
There are plenty of motels in the alleys across the street from the bus terminals and near the train station.