I am planning on heading to Seoul for 5 or so days at the end of October. Here are some of the things my friend suggested:

Some of the interesting things to do here are:

1 - You can go up about 1-1 1/2 hours north and take a
tour of the DMZ. They let you walk partway down
tunnels that have been dug by North Koreans. You can
also visit the truce village of Panmunjun where the
two sides hold meetings and from there you can look
into North Korea and hear the propoganda they
broadcast.

2 - About 10mins from my house is Gyungbokung Palace
which is an enormous palace that has been rebuilt
along with an interesting museum.

3 - There is a War Memorial near the army base that is
dedicated to the Korean War. I haven't been, but I've
heard it's very good.

4 - There are some large markets, both indoor and
outdoor and the night wholesale markets.

The food is also unique and fun to experience and
every day is somewhat of an adventure even though I've
lived here for a while. The city is easy to get
around in with an expansive, clean and efficient
subway system, buses, and taxis.

Good luck, let me know how goes...