It was a self-declared title and the mayor went along with it. As popular as games were back then, there was a stigma about them and most politicians wouldn't embrace them. I think they just got it because nobody else wanted it.
For arcade gamings epicenter, wouldn't it technically be Chicago? From Chicago Coin right up through heavy hitters like Williams and Stern. Funspot (Laconia NH) is probably it for arcade gaming today, and all the really big trade shows seem to be in California.
You could make the same arugment for the San Francisco Bay Area. Sega, Namco, Capcom, SNK, Atari, Exidy and a few others were there in the 80's...
Top that off with hundred's of arcades.
Matt
