On Saturday night I had dinner with my girlfriend at a restaurant that I had theretofore only visited with my school. It's one of Suncheon's quote-unquote famous restaurants, and is designated so by the government, and serves a few types of octopus dishes. If you visit 여수명신낙지 I recommend the 산낙지볶음밥, octopus fried rice, though it ends up being more like bibimbap.
It's excellent, and besides all the food you see there---including mustard kimchi (갓김치), a Yeosu specialty---you'll also get exceptionally-friendly treatment from the staff. The restaurant is in Suncheon's Geumdang neighborhood, behind Geumdang High School and about a block-and-a-half north of the Chinese restaurant 소평 other foreigners like. There's a street map here, in Korean. The 산낙지볶음밥 for two will cost 20,000 won. You'll be asked how spicy you want it, and I strongly recommend getting it mild.