If you want to eat cheap, one of the many useful things Russ learned when teaching English in Korea years back was to hit up a kimbap joint. For the first 'Korean meal' of our trip we went for the cheaper eats.
We found MyeongKa KimBap within walking distance of our place in Seodaemun. Kimbap places typically have an orange store front, just look for kimbap, or kimbab (김밥), or kuksu/guksu (국수) in the name.
We ordered KimchiBokkuemBap (김치볶음밥; kimchi fried rice) and Chijuh Ramyeon (치즈 라면; cheese ramen) with tteok-bokki (떡볶이; Korean rice cakes). The bokkuem bap was good and tasty, the cheese ramen was different yet satisfying. In Korea, the cheese typically used for cheaper dishes is American-style sliced cheese, so it adds a different cheese taste than what might be expected in North America or Europe.