I am an adult skater in Seoul, Korea and maybe I can answer some of your questions.
I would say most of the Korean cities have skating rinks and you can find coaches there, but the rinks in bigger cities such as Seoul or the nearby Kyounggi-do province (including Incheon, Gwacheon, Anyang and Goyang) and Busan may have better environment. If you choose to stay in Seoul, you are within 0.5-1.5 hour distance (by bus or by subway) to some 5+ rinks that offer figure skating lessons.
As for coaches available for lessons in Ensligh, I believe there are a few coaches who have been to US/Canada for training, so it would not be so difficult to find one... although not all of them may be willing to take adult skaters. Perhaps if you decide which city you would like to stay, I will be able to answer you in more detail.