There are many 'hang out' areas in Seoul such as Yeongdong, a largely residential area but with many local bars/lounges, and Itaewon, place to see non-Asian foreigners.
But my favorite had to be Gangnam and its vicinity. Its a trendy, youthful area to relax and have a drink. Great to watch the 'beautiful' and well dressed hipsters walk by.
Gangnam-gu (강남구) is the upscale side of Seoul. Considered to be more affluent compared to other districts, this is where you will find COEX, Apgujeong Dong (압구정동) Rodeo Street, Sinsa-dong (신사동) Garosu-gil (가로수 길), and Cheongdam-dong (청담동) Fashion Street.
Gangnam is still the business district where the famous Teheran-ro (테헤란로) is located, but some say it has also leveled up to a fashion destination, comparing itself with Myeongdong, etc.
For Kpop Enthusiasts: This district is also known as the location for headquarters of entertainment agencies, such as S.M. Entertainment and JYP Entertainment in Apgujeong-dong.
If you happen to be in neighborhood,Gangnam is worth to stroll around. After little more than a decade in the music industry, the thoughtfully named, highly affluent district of Seoul. This is not a place where I want to live. As this is the crowdest place I've see in Seoul. Good for a stroll and being curious around.
Besides, for a woman there are a lot things to do like shopping. You can spend a whole day shop from one store to another. Or just wander around and enjoy the view of skyscraper in district. This is one of the vibrant place in Seoul, where you find everything not only shops but many restaurants and bars. Each area of Seoul have different character.
After the very famous song of a Korean singer PSY-Gangnam Style, I was so interested to check what's really special in the area. Once we're out the metro station the first thing I've see is the stage of Gangnam style, standing in the street. The stage attract tourist especially kids.