One of my Favorite Areas in Seoul
What's NOT to like about this area?!
Personal favorites: 1) Walking around the Cheongecheon (literally an underground stream) at night, particularly when it's lit up by underwater lighting. Take the Gwanghamun, line 5, or City Hall, line 2, subway stations, and there are signs literally guiding you to it.
2) Kyobo Book Store (Gwanghamun station) is a MUST SEE - the best foreigner section (a.k.a. it's all in English) out of all the major bookstore chains. You might consider it pricy at first, but it's actually a lot less expensive than the others.
3) Go walk on the big piano near the Cheongecheon and you'll find Western restaurants like Bennigans and...Cold Stone Ice Cream (just opened last year)! They'll sing their songs in Korean or English, depending on what you prefer.