A slower Korea itinerary: Seoul, Busan, and Jeju?

We prefer alternating active sightseeing days with slower days and are looking at roughly two weeks in Korea. The first idea is five days in Seoul, five in Busan, and four or five on Jeju. Does that feel balanced, or would Gyeongju be easier than Jeju for travelers who do not want to drive? I would love suggestions for a comfortable pace with minimal hotel changes.