Gyeongbokgung Palace is on the top of my list with attractions of Seoul.
Gyeongbokgung Palace was built in 1395, however later was destroyed and then restored.
Besides the buildings of the palace, I enjoyed watching the ceremony of the changing of the guard, but probably I was more impressed by their clothes and weapons; very unique and colorful.
I was in Korea 9 years ago, in fall, and there were not so many tourists, what was very nice.
Changdeokgung Palace with its lovely Secret Garden is also a must-visit site in Seoul.
The other places I can highly recommend are:
-Bukhansan National Park
-Korean Demilitarized Zone (DMZ) located 60km from Seoul.