Summary
Good ol' Gifu, or 'GOG' as some might call it. Gifu is a great place to visit, especially if you're into leashed birds catching fish.
Seriously, Gifu's cormorant fishing is something to see. Charlie Chaplin reportedly visited Gifu twice because he was so moved by the display. Gifu has more than just fishing traditions though. There's the Giant Buddha of Gifu, Gifu Castle, and the Nawa Insect Museum. But probably the best thing to see (besides the cormorant fishing) is Shirakawa-go. A whole village of 250-year-old thatched roof farmhouses. Beautiful in the winter.
No matter where you end up in Japan, try to end up in Gifu at least once.