Most restaurants serve typical Korean fare, one main dish with a lot of side dishes. While the Korean restaurants in Muju don't stand out from one another, they're all fairly good, and reasonably priced a group of 6 can eat for about 40,000 won.
Imsil Cheese Pizza
If starved for Western style pizza, Imsil Cheese Pizza ìì¤ ì¹ì¦ í¼ì makes an excellent pie, and the owner knows the English names for common pizza ingredients. 16,000 won.
Nadeuri
For the ultimate in budget eating, consider Nadeuri ëë리. While it's a chain restaurant across Korea, the prices aren't standard, and in Muju 1000 won will get you one roll of kimbap, soup, kimchi, and radishes, with free refills on the side dishes. Even the more expensive items on the menu will only set you back 3000-4000 won.
Local food can be bought from the farmer's market, which meets on the 1st of every month, and every five days thereafter 1st, 6th, 11th, etc. excepting the 31st. Located across a few blocks in the northwest of town, you can't miss it if you wander in that direction.