I'm not sure if they are still around, but there seems to be a nice wall at the youth center (군산 청소년수련원 실내인공암벽장). It's at Songrung-dong 954-3 Daepyojeonha Phone 063-461-4166 (fax 063-461-3888). Not sure what the rules are, but someone there or at the wall might be able to help you out.
"If you can't do something well, you might as well learn to enjoy doing it poorly." -- from a de-motivational poster, but I find it oddly liberating!
My girlfriend and I are coming to Gunsan for a year from mid July. We will be working weekdays from 13:00 to 21:00, but looking for climbing gyms/crags/friends close by for during the week and weekends. Please let us know if you find anything good