The KTX from Seoul takes just 37 minutes to zip to Cheonan-Asan Station (W11000), but you'll need to connect to the painfully slow bus #2 to get to central Cheonan (30 min, W950). Alternatively, you can walk about 200m to Asan Station, where for W4700 you can get a 5 minute train ride into Cheonan Station (where you can connect to the Seoul subway)
Alternatively, ordinary trains on the Gyeongbu line connect directly to Cheonan Station in about one hour, making them a faster option for getting to the center of town. There's even direct through service for Seoul subway line 1.
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 is currently being extended from Cheonan Station to KTX Cheonan-Asan station and onwards to Asan, but is not operational yet.
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.
There are plenty of motels in the alleys across the street from the bus terminals and near the train station.