Likely there are no races this summer -too hot, there is the one in Kimhae through the mountain course in June.  There is the Korean marthon website, just type marathon in Korean in any Korean major website and they will give you a current list.  This is only available in Korean, I assume you know some Korean.  There were a few this spring in Haeundae and near Haeundae and there are currently 3 in the fall in Busan.  There are many running clubs in Busan these days, just join a club and they have their own running events, especially 5 and 10km races.  Many Korean companies and even universities have their own running clubs and will let outside people join.