Based on my experiences:

• Myeungdong market (LIFE WORK CAFE on Google Maps). Near the Myeundgong station.
• Gangnam station (on the #2 green line)
• Hongdae (Hongkik national university)— call street graffiti and college vibes
• Itaewon: traditionally where the US military was based, but apparently a new hip and upcoming area.
• Sinsa, Sinsadong
• Namdaemun market — there is also a good camera shopping area in Namdaemun.

The good thing to know is that Google maps actually works really well in Seoul South Korea. The bus and Subway information is up-to-date, very accurate and easy to navigate.