A quick trip to Japan? You can take a ferry from Busan to Fukuoka, Japan. Or how about a day trip to Tsushima island? If you want street food, the Yatai food stands of Fukuoka are pretty good.
In Seoul, perhaps catch one of the fun live performance shows? The Original Drawing Show is fun and you don't need to understand any Korean to enjoy it.
I've never been to Jeonju so I can't really say what there is to do there.