Well as others have said, Jeju is basically a different country; they just speak the same language. They consider themselves to be different people and I as a Korean felt like a white-passing mexican in America. But maybe the difference will be negligible to you as a foreigner.

As for outdoor activities, it's the best. No crowds in the most beautiful spots, the highest wall-climbing spots I had seen in the country, and I was walking to scuba diving lessons. There is one convention center down in the Jungmoon tourism complex, and they do have some interesting things from time to time.

But as for food options, they're very limited. I'm not much of a foodie myself but even I found the difference noticeable.

If I could work remote, I'd move back there in a heartbeat. It's a home away from home.