On the Honshu island, I've heard that the biggest rivalry is between Tokyo-Osaka-Nagoya. Tokyo and Osaka are home to the big banks/brokerage firms, Nagoya is the heartland of Japan's auto industry and home to Toyota.
I remember watching a Japanese TV series as child, and the characters talked about stereotypes people from Tokyo, Osaka and Nagoya had of each other; Tokyoites thought people Nagoyans had funny rural accents and were "unsophisticated" for lack of a people term; on the other hand, people from Nagoya thought their Tokyo and Osaka brethren were "greedy and pretentious" urbanites.