The area dates back 600 years or so and was once home to high-ranking officials and aristocrats. Bukchon is still residential although some hanoks have been converted into museums and guesthouses. Its a peaceful area which gives you some idea of what Seoul was like in the past (for rich people anyway) and is ideal for walking around. There are some good views from the top of the hill which were presumably clearer in Joseon times!
Bukchon street
View over Seoul from the top of the street
View in the other direction over Samcheong
Steps leading up to Bukchon from Samcheong
Getting there: the nearest subway station is Anguk. Follow the walled road which is directly across the road from Insadong-gil. Turn right and walk up the hill until you come to the Bukchon visitor centre. Various hanoks are scattered around this area, but to see the main concentration, turn left and the area above is on your left.