Busan is the kind of city that gets under your skin. Korea’s second largest city sits on the southern coast with beaches on one side, mountains on the other, and some of the best seafood in the country running through the middle of it all. My husband grew up here and if we weren’t based in Seoul, Busan would be home, which means I’ve spent years learning this city the way a local does rather than a tourist. This is the guide I wish existed when I first arrived. It covers everything from the beaches and the hillside villages to the fish markets, the best food to seek out, where…