The thing to remember if you want to visit Samcheong-dong for wandering around and taking pictures is this: GO EARLY. The little streets and alleys get jam-packed with tourists on the weekends and it can be kind of a nightmare, but it you go before 11am you can stroll around in peace. The stores and cafes start opening from 10am onwards.
How do I get there?
Anguk Station (안국역) exit 1 or 2. All the stuff you want to see is in the area immediately north of Anguk station, between Gyeongbuk Palace and Changdeok Palace, and stretching up to Samcheong Park. So, the opposite side of the road to Insa-dong. You could take a map, but it's more fun to just wander and get lost.
Pretty much all the main tourist attractions for 'traditional' or 'old Korea' style things are in this part of Seoul:
1. Visit the palaces
Gyeongbok Palace (경복궁) is the biggest and most popular of the palaces, and also the busiest. It's where you can see the Royal Guards procession. Changdeok Palace (창덕궁) is slightly less popular, but in my opinion much prettier, especially in Spring.
2. Wear a hanbok!
There are quite a few photo studios in this area for tourists to dress up in Korean traditional clothes (hanbok) and take pictures. But as I was walking around today I saw this hanbok rental place that actually lets you take the hanbok out of the studio and wear it while wandering around. The sign said they charge only 30,000won/day, with free entrance to Gyeongbok Palace. To get there, walk up the main road that goes around the east side of Gyeongbokgung, and you will see their sign directing you down an alley on the right.
3. Buy stuff at Insadong.
Insadong (인사동 거리) is where you buy all that crap like decorative chopsticks, hand-painted fans, Korean flag T-shirts and other gifts and souvenirs to take home with you when you leave Korea.
4. Visit a Buddhist Temple
If you haven't managed to visit one of Korea's more scenic temples, which are often out in the mountains, Jogyesa (조계사) is really conveniently located right near Insadong. It's also opposite the Templestay center, which is where you can go and get information about the nationwide Templestay program, if you're interested. There are lots of stores around the temple selling Buddhist statues, clothing and artifacts.
5. Observe a Confucian ritual performance
Once a year, on the first Sunday of May, there is a ceremony of special ritual music and dance called 'Jerye' (제례) at Jongmyo shrine (종묘). The shrine is located near Jongno 3-ga station (종로3가역).
6. Nurture your creativity with some artisitic inspiration
The National Museum of Modern and Contemporary Art (MMCA) is located right across the street from Gyeongbok Palace. There are also lots of tiny independent art galleries and museums nearby and around Samcheong-dong.
7. Learn some history
After taking in some modern art at the MMCA, go back in time to learn about Korean culture and traditions. The National Folk Museum, Palace Museum and Children's Museum are all right there at Gyeongbok Palace - There's loads to see at all of them, and entrance is free.
Although Samcheong-dong is known as an area for traditional and historical buildings, sadly there are more and more big businesses filling up the streets nowadays. Every time I visit, a new branch of some popular cafe or cosmetics brand has popped up in place of an independent store. I hope the area can retain its individuality and not end up looking the same as everywhere else.