Seoul was almost completely destroyed in the Korean War, leading the whole city to be rebuilt within the last sixty years - and rebuild it has! Seoul has become a modern megacity of skyscrapers with 10 million people alone within the city limits.
The key to a great trip or move to Seoul is finding those uniquely Korean sights and tastes within the city.
Hongdae Free Market
Vendors at Hongdae Free Art Market in Seoul (Katy Dutile)
Located across from the Hongik University, a top art school, Hongdae free art market is filled with indie art including handmade jewelry and 10 second sketch artist. It can be a little overpriced, but definitely worth a visit to pick up some nontraditional souvenirs. This market is only open on Saturdays, and after 6pm local bands perform. This hipster area of Seoul is also great for bars and nightlife.
Seoul World Cup Stadium
Seoul World Cup Stadium during 2007 Korea vs. Netherlands Friendly (Flickr/Connor Meagher)
Unlike U.S. stadiums, you can stock up on Cass (Korean beer) and bring it into the stadium to cheer on FC Seoul, the Seoul club team. Tickets for FC Seoul are 10,000 won (aprox 10 USD) for general admission, where the local's excitement is contagious.
Get tickets and check out FC Seoul schedule here: http://www.fcseoul.com/en/main/main.jsp
Tteokbokki, a traditional street food (Flickr/ Ten-ele-ven)
An important part of visiting any new city is trying the local street food. Try odeng (fish cakes cooked in a broth and drank while standing at the food cart), tteokbokki (rice cakes served in a spicy sauce), or for dessert, Hotteok (rice pancake with a warm filling of brown sugar and other deliciousness, varying by vendor). These food carts usually come out after 3pm and are open late into the evening
Myogaksa Temple Stay
For a two day, one night experience of monk life, try this cultural experience located on Naksan Mountain. Myogaksa Temple Stay includes prayer bead making, meditation, and waking up at 3:30 AM to the wooden bell, Moktak. It's an intense cultural experience, but leaving the temple you feel refreshed while simultaneously ready for a nap. This stay will set you back about 50,000 won (aprox. 47 USD), but gives the closest insight into Korean Buddhism.
Hiking Mt. Yongmasan
You don't have to leave Seoul to get some hiking in, although a halmeoni (grandmother) is likely to beat you up the hill dressed head to toe in top of the line hiking gear. This trail offers great views of the city skyline. For an easier hike, neighboring Mt. Achasan only take 30 minutes to climb and also gives views of the Han River. If you still want the view without the hike, head to North Seoul Tower on Mt. Namsan and let the elevator do its work.
Check out Visit Korea for other Seoul Hiking spots: http://www.visitkorea.or.kr/ena/SI/SI_EN_3_6.jsp?cid=309631
Soju (Flickr/Graham Hills)
While this may not be a sight, it's impossible to talk about South Korea without talking about Soju, which is similar to vodka. It's been said that Koreans are the Irish of the East, and after spending a day there it could be believed. One may be apprehensive about taking shots with dinner, but when in Seoul ... The most common bottle even conveniently pours to seven shots, then it's on to bottle number two!
Bukchon Hanok Village
Bukchon Hanok Village (Flickr/Jennifer Olmos)
Get away from the congestion and city life in Buckchon Hanok Village. In this village, you can view a beautiful example of traditional Korean houses without leaving the city. The homes are all privately owned, but there is an opportunity to stay in guesthouses in the area. After a walk around the village, go to Gyeongbok Palace or Changdeok Palace, both walking distance away.
Nanta Cookin takes a twist on the traditional Korean musical by using kitchen equipment. Bring the whole family to this non-verbal comedic show, where language doesn't matter. Be careful, the show gets messy for the front row and foreigners are often put on stage to help with the Cookin. There are three theaters in Seoul where you can catch a Nanta performance, including Myeong Dong, Gangbuk Jeong Dong, and Hongdae.
For tickets and performance times http://nanta.i-pmc.co.kr/en/index.asp
Traditional Korean masks in Insadong, Seoul (Flickr/Tim Walker)
This is the most touristy of the sights listed, but for the last day in Seoul, it may be just the right place to pick up all those last minute souvenirs. The center of this area is Ssamziegil, a type of spiral mall, filled with small shops of knick-knacks to bring home. There are also great restaurants in the area for traditional Korean fare.
Have any more suggestions? Feel free to share them in the comments below.