Small city gym, close knit-- they go on lots of trips, train hard (including annual climbing school) and are open to foreigners, though English is not spoken. They've had several foreign members in the past. Membership is subsidized and reasonable.
One story gym (4th floor) with steep walls (some with jugs) and a ceiling area with very high mats!
It's 5 minutes from the train station! Head down the main street that deadends at the station (there is an overpass to the R to cross the street that runs perpendicular). Turn right at the sign pointing the way to the Mokpo Taxation Office (in English). Across the street from the tax office is the smaller, nondescript Muan District Office, which has a small green sign in front that notes (in Korean) the climbing gym. If you reach the corner with the sign (also in English) pointing you back 35m to the district office, you've gone too far.