jxzy, you can take bus number 6011 or 602 that will bring you to Anguk station 9000won (one way) and you will be almost in front of the temples. For me it took around 60 minutes (just the bus ride) but I did it only once (yesterday ;))
However, for such a short time I would rather spend it walking on the main streets to see the atmosphere of Seoul, perhaps in myeong-dong (or something similar)
cheers!
To be honest, I'd go for either Changdeokgung, or Gyeongbokgung, rather than both. Changdeokgung has to be done on a guided tour which has a timetable obviously, and there are only two or three a day, whereas Gyeongbokgung you can just wander around yourself. There isn't that much between them to warrant visiting both if you only have a few hours. Jogyesa is cool, and very close to Insadong, which is nice for teahouses and crafts etc. All of this is within ten minutes walk of Jonggak station (Jongno).
aah, thanks for the great info! I had been thinking about Changdeokgung because of the famous "Secret Garden", but might just skip it then and focus on Gyeongbokgung. And those buses directly to Anguk sound great! I do want to see a little of Korean culture/heritage as opposed to "just walking the streets" (knowing myself, that would only lead me into shops and spending money anyway ;)
So, looks like I'm armed with enough knowledge now to have a few great hours in Korea, thanks again everyone!
I am with zt123 on this one. A 6-hour layover in Seoul is a bit risky. The bus on a Saturday took at least an hour to get from the city to Incheon when I had a 12 hour layover in Seoul this summer. Personally, I would use the layover to take a shower in the free public showers at Incheon and to chill.
don't forget that the airport (ICN) offers a variety of transit tours. The shortest is a 1 hour tour that takes you to a very peaceful nearby temple on a small hill, at the whopping cost of $5. It's very easy. After you pass through immigration, go down the escalators and straight to the transit tour desk. They have several other longer tours that may suit you, also reasonable, but usually require a group of people.
have fun!