I have 10 days in Korea in late October-early November, and figure I don't need to spend the entire time in Seoul. From what I can tell, most people spend additional time either in Jeju or Busan. My only other visit to Korea was a few days in Busan and I recall there not being much to do in late fall.

How is Jeju during this time? What would I have to look forward to compared to say, Gyeongju?