To improve your Korean vocabulary, I would suggest you try using free flashcard tools like
Beginner Korean app (https://play.google.com/store/apps/details?id=com.shex.beginnerkorean)
and
Topik Locker app (https://play.google.com/store/apps/details?id=com.shex.topiklocker)
Take the subway. Download an app called MetroidHD (https://play.google.com/store/apps/details?id=com.whitecrow.metroid&hl=en ), select Incheon Airport then Myeongdong. Follow the path. It is easy as pie and all stations have english instructions. Id also suggest going to Itaewon if you are english speaking. Has tons of clubs and eateries as well. From Incheon airport follow the path to the subway by turning right out of the gates and follow the icons to the subway (youll need to stop at the tickets booth and buy a subway pass, ~15,000Won will be enough). Will take you about an hour to either Myeongdong or Itaewon each way.
/edit six hours is plenty to enjoy either location.