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.
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.