After Busan, I went for a quick check to the towns of Pohang and Gyeongju before heading to Jeju island. Pohang it is a coast town with nothing specially interesting but have nice beach and views of the bay, also many parks around the coastline.
On the other hand, Gyeongju it is a very historic city, capital of one of Korean kingdoms for a long period. It has many tombs and historical remains and also a very nice historical museum where you can get a pretty good idea of the importance of the city.
About 40min bus ride from the town you can find a beautiful budist temple called Bulgoksa which is also situated on the perimeter of a national park with many hikes around. Unfortunately the temple it is very popular and large numbers of groups visit it. The temple opens at 7.30h so you have like 1.30h to see it quietly before the crowd show up. Walking around the tombs and the park it is very nice and pleasant so I totally recommend it!
Also in this two smaller towns I could feel that the people was warm and kind. I got invited to a coffee the night I arrived with a very kind man and we shared some nice words and gestures as the conversation was not very fluid.
The sunrise the next morning was beautiful and despite the industrial view the landscape was amazing.