There's a great mix of history and modernism in Seoul. Take it all in.
If you want to get out of the city, then hop on the metro and head to the mountains. Plenty of great opportunities for hiking just a short ride outside the city.
Take a cooking class and learn to cook such Korean staples as kimchi bulgogi.
Learn taekwondo, Korea's most popular form of martial arts. If you're not that adventurous, then be sure to take in a match.
If you're looking to stay a while and make a bit of money, then look into teaching ESL. Seoul (and all of South Korea) is one of the most popular places to teach English and actually make some good money doing it.
If you're a drinker, you've come to the right place. The Koreans can drink with the best of them.
Why you should add Seoul to your RTW travel list
Don't let the modern buildings fool you: Seoul is an ancient city
Eat awesome Korean food and other cuisines with the locals
If you need out of the city, it's easy to get to the surrounding mountains
See old temples such as Chogyesa, Pongwosa and Hwagyesa
Celebrate New Year, twice a year, in January and February
Why you should not add Seoul to your RTW travel list
Seoul can overwhelming and confusing for visitors. It's easy to get lost, and even the locals have a tough time giving you the right directions.