Gogung (고궁) is a famous restaurant in Myeongdong and famous for their… yes, Bibimbap. Specifically, they feature Jeonju (전주) style bibimbap. Jeonju is a city located in the center of South Korea and is famous for iteration of this dish. As far as we can tell, Jeonju style bibimbap simply features a more diverse variety of vegetables.
Hidden away in a small alley near Anguk station, Jaedong Sundubu (재동순두부) is popular even among the locals. The restaurant serves a variety of traditional Korean dishes, including Sundubu, Bibimbap (mixed rice), Kongguksu (noodles in cold soy milk broth), Pajeon (scallion pancake), and Korean BBQ.