If you are more into Korean Traditional Tour there are places in Seoul to see but if you really really want to only see and hear and smell the culture than I'll lead you outside of Seoul to Andong village.
It's Also the place where in 1999 England Queen Elizabeth the II visited
It took me a while to gather my courage inorder to decide to introduce Andong because expalining by words and picture of how to get there is a problem
HOW TO GET TO ANDONG VILLAGE!
You need to get to a Large Bus station Called Central City(Yup Korean love English), the Closest Subway station is Bus Terminal Station (고속터미널역) it's subway line 3, you could get there by the blue bus 142, 642, 148.
Now you need to get a ticket for this. You can go online to order or go to the ticket booth to buy. Ask for Andong. The online doesn't have English version so I advice you to have someone who is fluent in Korean or you will be lost for sure.
Once you get there you will notice alot of bus lines but no bus....In Andong there is only one bus/hour
Obviously you sould choose the Taxi for transportation.
Congradulations you arrived in Andong.
NOW WHERE TO GO?
-In Andong you should visit the street market, cheap and delicious food is waiting for you.
Get on a texi and go to Andong Gu C Jang.
-Go taste the Famous Andong Jim chicken! It inside the Andong Gu C Jang. Here the link to the Review I've wrote
- THIS IS A MUST THIS IS WHY I'VE BROUGH YOU HERE: Visit the Hahoe Folk Village, Get on a cap and say Hahoe, you need a ticket to go in. It caust 3,000wan
You can book a home to stay if you want to experience living in Korean traditional house. There is a small street market inside enjoy shopping. You can experience Korean Tea and how you drink it gracefully, you mostly will stroll and enjoy the view. I will not explain any more because I blieve exploring the unknown is one of the Traveling Enjoyment Secrets.