Seoul has a LOT of things you can do, below is a quick list of thoughts:

1. Markets: Seoul has a few really good some what old-style markets that are fun to walk through. Namdaemun market is a fun market with all sorts of stuff from clothes to food to household goods. Dongdaemun market is great for clothes, fabric, all sorts of craft stuff for craft projects. There is also a reclaimed stream running next to the market that is a great place for an evening walk. Next to Namdaemun is Myeong-dong. There is are a couple of big Korean dept. stores there (Lotte and Shilla) and is a very fun open-air mall type of market with all the modern int'l clothes brands as well as the local brands, make-up shops, etc. The street food scene there is AWESOME and is another good place to go in the evening. The last good market to go to is Insa-dong. Good food here and a lot of antique shops and Korean art shops. Great place for some cool Korean souvenirs and food.

2. Parks: Just south of Myeong-dong is Yongsan Park, you can walk-up or take a cable car (recommend the car, but lines can be long) to the top and get a great 360-degree view of Seoul. There is a tall tower you can go up as well, or just walk along the paths and get some great views during day and especially at night. There are several ancient palaces in the city, too. Kyungbook-Gung is the historical center of Korea gov't (kind of like the Forbidden City in Beijing, but smaller) that has gone through a lot of upgrades over the years and is a really cool place to go. Big grounds that are nice to walk in and take a break from the loud city. There is a cool museum in the very back of the grounds as well. There is another palace right next to city hall, but can't recall the name that is also nice.

3. Take a day and to the USO DMZ tour. It is the best tour of the DMZ and is worth taking a half-plus day to do. The hotel you stay at should have the info, or search it online as I think you need reservations. It boards (or used to) at Camp Kim in Seoul and takes you up to the DMZ. You get to go into Panmujon, where they have the negotiations, see into N. Korea from a park near there, and also take a tour of one of the tunnels they dug to infiltrate South Korea. Great tour and worth the time.

4. If you want to see the "night life" of Seoul, head to Gangnam-dong in the evening. Crazy busy with all sorts of shops, food, movies and Samsung's global HQ. A really fun place to just go and "people watch" and get a good feel for the vibe of the city.

5. If you have time, Itaewon is kind of fun, but it would be the last place I would put on the list. At the south-end of the base, there is a really cool Korea History museum that is worth spending some time, and the Korean War museum on the north-end is also worth it. The area of Itaewon itself is not that great compared to all the other things to do in Seoul (in my opinion), but is a great place for international food.

A couple of things to note:

1. Summer is dreadfully hot and humid in Korea. It is a race to 90 between heat and humidity, so take that into account. Take lots of water with you when you are out and about.

2. For transportation, get a good subway map at the hotel and you can get anywhere quickly and cheaply. Taxis are fairly cheap in Korea (don't take the black taxis! They are pricey!!) and good to get around in, but traffic in the city can be really bad, worse than any place I have been in the US except maybe LA. The subways are clean, have good AC and have stops everywhere.

3. Don't worry too much about language. All signs are translated (way more so than Japan) and it makes getting around easy. Most young people speak some basic English and as a people they are very friendly and happy to help if you have questions or need directions.

4. Go local for the food. Korean food is awesome! Not just the fancy Korea BBQ stuff, but the local street food, hole-in-the-wall shops and all are usually pretty good and pretty cheap.

5. Korea has a great bus/train system if you want to get out of the city, but there is a lot to do in Seoul as well, so may not be worth taking the time. If you are flying from Japan to Seoul, take the downtown airport in Japan to Kimpo airport in Seoul ICN (Incheon) is a great airport and you will fly out of there back to the US, but it is about an hour outside the city. Kimpo is in the city and will be closer to hotels and things to do. You will save a couple of hours by using Tokyo's older city airport flying to Kimpo than going from Narita to Incheon.

Hope you have a great trip!