There are free lessons given at the Suncheon Education Office from 7 to 9 on Tuesdays and Thursdays. The levels are beginner and intermediate.
In a taxi just say "교육청" or "Gyo-yook Chawng." If you're new to Suncheon it's a little hard to explain where it is, but once you get there you'll be able to see where you are. If you know where the coffee shop "Java Dave's" is, you'll see that park across the street, and the Office of Education is on the other side of it.
The lessons are a little dull and dry, but pretty standard for free Korean classes.