3 week itinerary for Korea

Hi, I am going to visit Korea in may for around 3 weeks. I am planning to visit Seoul, Busan and Jeju and would like to have some feedback on my itinerary. I tried to make the trip relatively relaxed to have room to roam around and also keep the day of travel free.

Can you give me some feedback? Am I missing something in my plan that is a must see? Are some days to hectic/empty?

Thanks in advance!