Wife and I have a trip arriving in Seoul on August 24 and departing from Busan nine days later.

What would be a reasonable amount of time to spend in Seoul on arrival, and what towns should we visit on the way to Busan by train or bus?

We have been to Korea once before visiting Busan and Gyeongju for about four days each. Loved both places, including the mountain walks.

I am trying to pin this down soon because we like to stay at Hiltons, and they have a 50% off sale for Japan and Korea beginning June 2. (Besides Seoul, there is also a Hilton in Gyeonju, which we liked.)