I'm not sure why this restaurant has such a high rating on VegGuide. The menu doesn't have anything inherently vegan or vegetarian; all of the tofu dishes contain seafood, the menu is more than a bit confusing, communication about ingredients was a chore and constant worry, and there's no ambience. It's super popular with Korean students and some adventurous Americans but doesn't try at all to attract newcomers to Korean cuisine (I'm not a newcomer, but I'm not well-versed, either).
Ultimately, using tips from previous reviews, we had a vegetarian dumpling dish ($6) which was edible, but not very flavorful on its own. Also, my friend and I were both confused and worried about the ingredients, as there are small chewy, roundish balls that looked like some kind of meat. When we asked, the answer was that they were dried radish. If I had to guess, it was texturized vegetable protein (I hope) or something I'd rather not think about. I still don't know.
We next had a Tofu Jorim (~$10), also at the suggestion of the previous reviewer. This dish wasn't on the menu, so I'm glad my friend had remembered the name of the dish. It was okay, but also not terribly flavorful; there was no "sauce" per se, it was served luke-warm and it was basically just tofu with green onions and red chili, but had no kick to it whatsoever. It came with a meager portion of super-sticky and compacted white rice, which was not impressive.
Finally, we had a noodle bowl dish, the name of which I can't recall (also ~$10). It was not good. It consisted of tofu over long wheat noodles, covered in a black-colored gooey sauce that had a bizarre flavor---not sweet, not smoky, not salty. I don't know what it was, but it was not something I cared for after a few bites.
The side dishes and pickled foods were pretty decent, especially the eggplant and the kimchi.
This place gets packed at peak hours, so avoid it then if you don't like crowds. I wasn't a fan of all the styrofoam and disposable utensils either. I also didn't like the cafeteria-style service, where you order and pay, wait for your number to be called, eat and then have to bus your own table.
In the end, this place makes me even more suspicious of the vegetarian credentials of Korean food. It's a shame, because dishes at other tables looked really tasty and fresh, but they all had meat. If they could replicate that freshness vegan-style, I'd be back in a hurry. I'll try again, because I think Korea Restaurant can make good vegan food if I knew how to order it, and the service is friendly enough. But if you are vegan or vegetarian, and know nothing about Korean food, do not come here.