From Hongdae, the commute is roughly an hour and a half, but do give yourself more time to get there. We transferred from Line 2 (Honggik Station-->Sindorim Station), to Line 1. Once you transfer to Line 1, pay attention to the actual stops because not all of the trains go directly to Incheon. Some of them loop around, completely bypassing the Incheon segment. If your train is not headed towards Incheon, transfer at Guro Station to another train also on Line 2, but specifically Incheon-bound.
Once you get off at Exit 1, and The bright red gates of Chinatown will be right across the street. Once you walk through the gate, you will immediately see restaurants lined up that all advertise the same thing--Jjajangmyun (aka Chinese-Korean Black Bean Sauce Noodles), a Koreanized take on a Chinese noodle dish. I initially wanted to find the restaurant where they filmed the jjajangmyun delivery special episode of Running Man (a Korean variety/game show), but ended up eating one of the first few grander restaurants instead. It just so happened that it was a filming spot for another variety show, Infinity Challenge. Their menu has bough Chinese and English on it. We ordered 2 rice dishes (Mapo Tofu over rice (8,000 won) and another meat and vegetable dish (12,000 won)--forgot the name), the classic jjajangmyun (5,000 won), and tangsuyook (22,000 won), which is sweet and sour fried pork with onions, carrots, and pineapple. The rice dishes came with a spicy seafood soup, which I assumed was a similar soup that they use for their jjambong (spicy seafood noodle soup), which is another famous Koreanized Chinese dish to try in Korea.
As we explored the area, shops also sold an interesting puffed cookie shell. There were variety of "mooncakes" with different filling, egg tarts, coconuts, rainbow slush, and ice cream cones.