War Memorial. A great museum (though you might want to skip the first floor if pressed for time). I learned a lot about the Korean War. I came close to crying quite a few times. Make sure you read the story about the 10 soldiers. The stature in front of the museum of the two brothers (the older an officer for the North and the younger a soldier from the South) embracing on the battlefield is really moving.
Fondest memory: South Koreans are very friendly (remember I live in Japan). Many strangers came up to me and said "Welcome to Korea" or asked me how I liked the country. I really felt welcome.