I found another coffee shop that has soy milk: Caribou Coffee! I don't know why, but of all the chain coffee shops in Korea, I never thought to check out Caribou - duh! There really aren't many locations though.
The interior is pretty big and it seems that a lot of students come here to do their studying, since it's right by a Womens' University. They have a big selection of drinks, and they even have decaf coffee, which is a rare thing in Korea. I got their soy chai latte (small size = 5500won). It was pretty much the same as Starbucks' soy latte, pretty sweet and concentrated. Perhaps next time I'll ask them to leave out any syrup that goes in it. One minor gripe is that they only have two electrical sockets for people to plug their laptops in- one on either side of the coffee shop. It might look like there are more throughout, but trust me, those don't work (I tried and even asked). So if you need to charge your laptop, you better grab a spot close to one of these outlets. WiFi available.
Fresh fruit in cups.
Directions: Sinchon Station Line 2, Exit 4. Walk straight, pass Coffee Bean, and On the Border. You will see Caribou Coffee on your left.