Hello depth,

There's an organization currently located at City Hall that offers free Korean classes. It's called Busan Foundation for International Activities. However, I went there a few weeks ago, and they told me that since they're moving their office to another building (apparently just across the street..?) they won't be starting up Korean classes again until beginning or mid-March.

This is the site where you can get a little more information as well as the application for the classes: http://www.bfia.or.kr/english/foreigner3_2.html

Best of luck!