Haven’t written too much about life in Korea in general, but last week someone chalked up the cultural and job issues here to being akin to living in the “wild wild west.”
In essence, as a foreigner living here the rules are bendable and the hogwon system is dicey.
Korea is not the wild wild west. Korea is a great “gateway drug” of a country to work in as a first foreign country, but life here is more silly than crazy and life here is not characterized by lawlessness and spontaneity, but rather the opposite.
Things here can at times be very mechanical. I think the educational system here is a bit like a Rube Goldberg machine, particularly the English-teaching facet. The focus is on keeping the students as busy as possible, even if the end result after years of “learning” is a giant turd.
In many ways Korea is a forward thinking nation, particularly on the mainland, but Jeju architecture for the most part takes its cues from Soviet-era big box style. Even new apartment complexes are these horrifying ugly boxes. There doesn’t seem to be a big focus on urban planning, even though Jeju is leaning towards overdevelopment, which would be tragic because the island has such natural beauty.
But more importantly, life here is incredibly easy, which allows people to be complacent. You don’t have to learn Korean to thrive or be part of a community. Small issues crop up here and there, there is a little bit antagonism against foreigners but nobody really acts on their prejudice except to stare and make frowny faces at you.
The biggest issue with racism that I’ve heard about is a landlord refusing to offer housing to a western couple, which is wrong but not egregious.
Most jobs foreigners get here pay on time, and pay well enough to offer a wonderful lifestyle.
There are no threats on your life here, technology is great here, no questions about internet access or phone communication.
Korea does not have to be a challenge.
But the country needs more bagels.
Culture Time 
Well, there are the issues of indirect communication, which can be tricky for some, and dogs being viewed like goats or something, and for profit schools that can’t afford any discipline. But we found Koreans in general to be friendly and helpful, and Jeju generally modern and beautiful (the natural sites, as you said). Too bad the hogwons don’t try to teach Korean to the English teachers, which would help the students and the teachers greatly.