I wanted to try a bunch of unique food while visiting Korea's baseball stadiums. Unfortunately, most of the offerings were pretty standard. One thing I noticed was the availability of instant ramen and plenty of hot water to make it. Most concession stands also sold drinks and simple snacks, but there wasn't very much along the lines of unique dishes.
Along the edges of stadium parking lots at several ballparks I found stalls selling freshly fried chicken. For $5, you got a decent meal, or for $10 a very filling meal complete with a beer.
It's not terribly unique, but it's very delicious, especially when fresh, and certainly filling. I saw several attendees at the game eating their chicken as well.
I should note that you're generally permitted to bring in whatever food you'd like, similar to Japan. At least one stadium offered in-and-out privileges through at least one gate, which was right across the street from a convenience store. Prices inside the stadium weren't too high either.