There is sooooo much good Korean street food in Seoul! As an enchanted tourist, some of my favorites are below.
The first one is an egg on what tastes like corn bread called, aptly enough, egg bread (GYERAN BBANG). This was a little stall in the shopping district of Myeongdong outside of hotel. They are a delicious combination of savory and sweet and a perfect breakfast snack. I found a recipe for making your own here: http://mykoreankitchen.com/korean-style-egg-bread/.
My next favorite snack from a street stall was a cup of rice cakes (tteokbokki) doused in hot sauce called gochujang. Tteokbokki is chewy, spicy and oddly satisfying to eat. This particular cup was peppered with small slices of fish cake.
Also in Myeongdong were these adorable dressed up ice cream dishes skillfully scooped to look like a budding rose with chocolate, green tea and strawberry cream. Like the kid in the picture I desperately wanted to try one but the line was always too long at the Milky Bee.
Other favorites were cups of fried sweet potatoes and fried, fish-shaped bread (not filled with anything fish but with red bean paste). They were so good!
Innis Free (everywhere), Tony Moly (best packaging), Skinfood, Too Cool for School and Etude House were my favorites for quality/affordability balance. Literally hundreds of cosmetic stores line the tourist and shopping areas in Seoul. Save some space at the airport for duty-free items. Most stores will give you at least one free sample--to score more, go directly to the stores and go in the mornings before it gets crowded. If you spend a lot in one place, you may get full-sized items as samples or even cute tote bags like the one I got below after spending a bunch at Tony Moly!