The local specialties are pheasant and rabbit, hawked by every restaurant in town, but you'll need to fork out W30,000-50,000 for a serving feeds two or more. A more affordable option is sanche mountain vegetables.
Jeonju Sikdang
near Suanbo Hi-Spa
Does a good sanche bibimbap for W6000 and sundubu tofu stew for W5000.