Suanbo has a thousand years of history and has long been a favorite of Korea's emperors and presidents. Alas, not much has been done here since the 1970s, and the most attractive thing about the current incarnation is the location surrounded by mountains.
Local buses 240 through 246 connect from pier 3 in front of (not inside) Chungju's bus terminal to Suanbo in about 40 minutes (W1000). Follow the crowd and get off at the first stop in town, which is near the tourist information office.
Suanbo is small enough to cover on foot, which is good, as there are no other options anyway (aside from the occasional taxi from Chungju).
Suanbo is a hot spring town, so the thing to do is to go hot spring dipping. Most all hotels offer entry into their spa for W3000-5000, but it's worth it to make the 15-minute hike up to the Park Hotel on the western outskirts of town, which has the best views and the only outdoor tubs in town (W6000, open 6 AM to 9 PM; separate facilities for men and women).
In winter, skiing at the nearby Blue Valley Resort (2 km away) is a popular option.
A market near the river sells all sorts of local specialities and handicrafts.
The local specialties are pheasant and rabbit, hawked by every restaurant in town, but you'll need to fork out W30,000-50,000 for a serving (feeds two or more). A more affordable option is sanche mountain vegetables.
Suanbo has a glut of accommodation, most of it in older, grottier concrete behemoths from the 1970s, most of which will give you a room for around W30,000/night.
The tourist information office is in a little Korean-style hut in Multang Park, near the intercity bus terminal. Some English spoken, and you can pick up a handy town map from here.