https://goo.gl/maps/7LhoR2YEDzCMq6dY9
There are some lists of museums. Some of them are free. If you are interested in local history, I recommend to visit these.
Personally, I like the Museum of Modern History of Korea in Heyri Art Village.
In this place, you can see how Korea has developed last several decades. Many of items are from the real time collection therefore the exhibition is very vivid. I could even find Louis Vuitton Bag of 1970’s!
When I visited with a friend who was adopted aboard, she could understand how much Korea was in a bad situation economically after the war. She could not find her biological family when she visited Korea, but at least she started to understand why she was sent to another country when she was born… I was stunned to hear her story at this museum, but it was good opportunity for my friend to understand Korea more.