My award ticket to Seoul allows to add a domestic flight in Korea for free.

I'm staying in Seoul for a week so for the sidetrip I'd probably fly out in the morning, stay overnight and go back to Seoul late evening next day.

Which place would you recommend going to in such a way? Busan, Jeju or somewhere else? Travel is in June and I like nature as much as cities (as long as they are not rows of bland concrete boxes).

Thanks in advance!