Being a foreigner in Korea means you can drink if you are 19 years old instead of waiting until you are 21 back in the States. Since I recently turned 20 here, we hit up a bar that was popular among foreigners, called Thursday Party. You can get there by heading down the big street a block further than Exit 9 of Honggik University Station. Turn right on the alley where the fruit on a stick stand is (leads you to the street shopping stores) and keep going until you reach the end of the block past Inssum Club. Then turn right and walk 2 blocks down, and the bar should be on your left.
The bar also has a few games inside, such as darts, foosball, and beer pong. Beer pong costs 10,000 won for 2 pitchers of beer. We ordered some of the lighter drinks, Midori Sour, Blue Hawaii, and a frozen strawberry margarita, a total of 27,900 won. The bar was a fun place to chill, talk to friends you came with, and even meet new people! We ran into a group that also happened to be from the Tri-state area, one was from NYC like us too! Starting out at a more foreigner-friendly bar would probably be easier for a first-timer because they are more open to conversing with strangers, whereas in a more Korean bar, you might get a few glares for trying to start a conversation.