South Korea is entirely safe. People are living safely on the Island of Japan now, which is much closer. The danger radius is in the area of 20 miles from the site, South Korea is nearly 1000 mi away
Better take a Geiger counter with you or rent one there, or at least take a radiation badge. I doubt that the governments will tell you the truth. I recently read a blog on the subject by a Dr. George Thomas at his blog location at http://www.ghthomas.blogspot.com.
Other people asked questions on similar topics, check out the answers they received:
Other people asked questions on various topics, and are still waiting for answer. Would be great if you can take a sec and answer them