This bakery/restaurant/cafe called 'Mix & Bake' is located in front of the Seoul Olympic Park. Since they don't provide soymilk, I just bought my own at a convenience store nearby, and added it to the coffee myself. Don't judge me for not being able to drink my coffee black!
Didn't really look at their food menu, so I'm not sure whether they have veg options... doubtful. I also doubt any of their baked stuff is vegan. :( Interior is clean and spacious though, and it's right next to the park. :)
Directions:
Mongchontoseong station on Line 8
Exit #2, walk less than a block and you'll see it on your right.