The place I love to go to is over by Hapjeong Station. It's behind the Holt Building. I don't recall the name of it, but I'll have to head over there sometime for I remember they have parboiled potatoes in that dish along with some watermelon.
Another safe place to get it is at Myeongdong Gyoja. There they have healthy green noodles. Here's something I wrote on the Kongguksu there a while back:
Kongguksu 콩국수: Kongguk is a chilled soy milk noodle soup. Traditionally, it's a refreshingly hearty bowl filled with wheat noodles, soy milk, cucumbers, and ground peanuts. There are variations of this dish. I have had it with watermelon, parboiled potatoes, pear, and various other ingredients. My favorite version can be found at Myeongdong Gyoja. Here the noodles are green because they are made from the super healthy chlorella algae and green tea. These noodles are full of protein and vitamins and have plenty of life in the thick soymilk broth. And, best of all, this dish is vegetarian friendly.
Myeongdong Gyoja: Myeongdong exit 5. Make a left at the first intersection (Woori Bank) and make the next right (Who.A.U. Clothing Store.)