I am taking red eye flights to South Korea (arriving October 22, Satuday, 8 AM; departing October 30, Sunday, 7:30 PM) and want to split my week between Seoul (4 days), Jeju (3 days) and Gyeongju (2 days). I want to take in both culture and nature and do not want to overdo seeing every magnificent ancient palace, temple and fortress out there. Can I get people's advice on how to arrange the trip, including transfers?
So far, I was thinking:
October 22 (Saturday) -23 - Land in Incheon Intl at 8 AM, two days in Seoul
October 24 (Monday) - Take a Jeju Air flight from Gimpo Intl in Seoul to Jeju
October 24-26 - In Jeju
October 26 (Wednesday) - Look for an evening flight from Jeju to Ulsan (any advice?), transfer to Gyeongju
October 27 (Thursday)-28 - Go around Gyeongju and Seokguram
October 29 (Saturday) - Look for a morning flight or train from Ulsan to Seoul
October 30 (Sunday) - Fly out of Seoul at 7:30 PM
What do you guys think, and can I get input in the transfers above to and from Ulsan?
If it helps, these are the places I was hoping to hit.
Seoul (4 days)
Seoul Palaces
- Changdeokgung, best palace?
- Gyeongbokgung, changing of guard
Bukchon Hanok, old homes
Cheong-gye-cheon riverside walk
Jongmyo/Changgyeonggung tranquil grounds
Namsan/Seoul Tower
Dongdaemun Park
Inwangsan / Seoul Fortress Wall
Leeum Samsung Museum
Natl Museum
Noryangjin Fish Market
Hongdae
Jeju (3 days)
Manjanggul lava tubes
Hallasan
Scooter around coast
Gyeongju (2 days)
Seokguram grotto
Gyeongju museum

