Of all the kid "cafes" in Jeonju, this one was the most no thrills. In Korean it is "피터팬스토리 전복지사."
It was in this warehouse-style place, and a little drafty. Not as cozy or as new feeling as some kid cafes, but for keeping my toddler happy for a few hours, it did the job. Near the register is a little hamster, which ended up being the most interesting to my son for the last 20 minutes we were there.
Address: 전복 전주시 완산구 완고을로 62