Sinsa Market Tteokbokki
My mother introduced this place and is a frequent customer- it certainly is a place I'd recommend more to Korean locals than to foreigners, as it leans more toward nostalgia than modern with its taste. But it certainly doesn't mean the taste cannot be appreciated by newcomers to Seoul.
The exterior might throw some off, as the area itself (Gangnam) is known for affluence. The building has a wooden door that almost seems too flimsy for use, and a cruder sign that nervously alerts of its existence and purpose.
It's only when you are past the door and lead inside the restaurant that you see the traces of Gangnam in passing and staying customers.
I recommend that you try everything on their menu, but of course if anything please do try their spicy rice cakes with the dumplings. If you're new to this type of dumpling you'll react as I had at first: surprise at the lack of filling then yearning after a month later for the same fried sweetness.