check out the touristy places like gyeongbokgung, dongdaemun, myeongdong and insadong. also id recommend hitting up apgujeong rodeo and sinsa (garosu-gil) if your around gangnam. seeing as your coming in december, make sure to bring a thick jacket. it's crazy cold in winter.
if you want to party, itaewon/hongdae/gangnam are good areas. i'd recommend m2 (hongdae), boombar (itaewon), ellui (gangnam), answer (gangnam) and octagon (gangnam). if you want a cross between a bar and a club, then goto ho bar (there's tons everywhere)...it's like $70 and you get a bottle, a table and service (snacks).
oh and make sure you grab some $1 soju's from the convenience store and prepare to get completely destroyed before you go out at night. it's the way to do it.
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