It's my honor recommending you the places to go in Seoul, my hometown!
I wish my best for your visit to be phenomenal!
I categorized places from 4 stars(must go) to 1 star(a light recommendation)! and I also added public transportation(subway) information too!
**** Kyungbokgung Palace
There are 5 palaces in Seoul, and among them, it's the main palace of Joseon Dynasty that was used from 1392~1592 and 1865~1895. And it's the palace that represents Seoul in 21st century at the same time.
Nevertheless many traditional architectures had been deconstructed during the annexation of Imperial Japan from 1910~1945, still various buildings have remained and it's still aesthetically beautiful. Furthermore, you might be able to see the blue house, the residential place of president of Korea.
https://www.youtube.com/watch?v=rpYq1lSce1U
the gangnam guy, Psy's music video, "korea" was taken in this place. If you want to see how the palace look like ahead of visits, it's a really good idea to watch this video.
*** National Folk museum of Korea
It's inside of Gyungbokgung palace. The tall pagodas are now used as a museum.
so it's really easy to acess!
Nearest station, Gyeongbokgung Station, Line number 3
so it's really easy to acess!
** Deoksugung Palace
Deoksugung palace is the most recent palace that was used in Seoul. The last Emperor of Imperial Korea was residing here until 1919. The harmony of European Gothic buildings, Korean traditional palace buildings, and 16th century Korean nobility's mansion is quite astonishing. It is right next to Seoul City hall.
Nearest station - Seoul city hall station, line number 1 and 2
This is Seoul city hall. If you have no idea where to go, just saunter around the city hall and you will find something. (All the tour place is near here. Since it's in the middle of old downtown area)
**** Seoul National Museum
Abbreviating, but never exaggerating, "4000 years length of History of Korea" is right here.
Nearst station - Ichon station, Line number 4
*** Insadong
Mecca of shopping for foreigners. You can find so many traditional souveniers around here.
And if you go into small alleys, you can find the atmosphere of 1930s~ 1970s of Seoul.
Nearest station Jonggak Station, Line number 1
*** Seoul Station and Namdaemun
When Seoul was surrounded with wall, Namdaemun was the door that everyone had to pass by. At that time, wall was about 2m higher, and it was the first place that the cirt train passed through in 19th century. Right next to it(about 5 minutes away on foot), Seoul Station is standing. It was also constructed about 100 years ago and the old platform is now used as a museum of Seoul Public transportation.
Nearest station - Seoul station, Line number 1,4
**** SamchungDong, AngookDong
From traditional buildings of 19th century, to the modern architecture that was built yesterday, the harmony of these small houses are great. It's a great idea to look around the small alleys too! The only demerit of this place is, that it's on the hill. It's in between Kyungbokgung Palace and Changdeokgung palace.
Oh, by the way, at the end of the hill, you can find my old highschool!
Chungang Highschool, my "alma mater" !
Nearest station : Anguk station, Line number 3
** Myeongdong
The mecca of shopping in Korea. There is literally everything.
Also, it has the oldest cathedral of Seoul that was constructed 150 years ago.
Nearest station - Myeongdong station, Line number 4.
* Korea University
Korea university has the same status of Yale university in the United States.
It's one of the best universities in Korea, and furthermore, the campus is old and beautiful!
Station - Korea university station, Line number 6
*Songdo International city
I am not highly recommending this place to visit since you can see these cities in the United States too very often. It's a small version of Chicago in Korea.
Though it's really close to the airport, and it's a really good place to chill out during the day I think.
It takes about 1~2 hours from Seoul.
Nearest station - Songdo centralpark Station
These are my preliminary recommendations to visit in Seoul, Korea.
And I highly recommend you to download an application called "Transit"
It will guide you to the place that you want to go in a fastest way!
Hope you to enjoy the trip!