When I was going to school in Shinokubo, the Korean town of Tokyo, the teachers seemed to pretty much eat at Incheon, a Korean restaurant nearly every single day.
One day I went with them and I had this Yukkejan which is this very spicy Korean soup. In fact one time we had Yukkejan at Seoul House and it was so spicy that the Korean students that were with us couldn't finish it! My friend Jason put them all to shame by gobbling all his up and asking for more 😛
If you want Korean food, especially around lunch time if you can make it over to Shinokubo, just one stop past Shinjuku on the Yamanote line, you should check out either Incheon or Seoul House.
As you come out of the station walk under the bridge and continue walking down the street. When you get to AM/PM cross the street go down the alley, the first little place on the left is Incheon. Or, at the AM/PM, cross the street but continue walking down the main street about 2 or 3 more minutes. Keep your eye open for Seoul House, it's in the basement of building that also has an internet cafe.