New York is the City That Never Sleeps or the Big Apple. Chicago is the Windy City. Paris is the City of Lights. Sayings like this, that try to capture the spirit of a place in a short phrase, exist for Japanese cities too.
A common saying about Osaka is 食い倒れの街 (kui-daore no machi), the town that loves to eat. 食い倒れ means to eat until you drop. This is probably true...Osaka is known for great, cheap eats and is the birthplace of famous street snacks like takoyaki and okonomiyaki.
A lesser known saying takes the phrase and applies it to Kyoto. Kyoto people are generally held to be very おしゃれ (oshare, pronounced o-SHA-reh) or fashionable and well dressed. Therefore, Kyoto is 着倒れの街 (ki-daore no machi), the town that loves to dress up. Kyoto is famous for its beautiful woven kimono silks or Nishijin-ori. People in Kyoto still wear kimonos quite a lot in their daily lives, probably more than in other cities.
An even lesser known saying apparently exists about other cities. Nagoya is said to be 貯め倒れの街 (tame-daore no machi) - the town that loves to save money, or another way of saying Nagoya residents are cheap. Osaka people are generally said to be rather tight with their money too, and often are called the Scots of Japan. (Just as in any other country, various regions of Japan take friendly snipes at each other all the time.) Nara is said to be 寝倒れの街 （ne-daore no machi) or the town that loves to sleep, since the shops there close up fairly early and there's nothing to do (according to some residents) at night.
I haven't really been able to find one phrase that is applied to Tokyo though. I've read 飲み倒れの街 (nomi-daore no machi) - the town that drinks until it drops, or 履き倒れの街 (haki-daore no machi) - the town that loves...shoes? (The last one is also applied to Kobe for some reason.) My favorite -daore phrase applied to Tokyo though is 行き倒れ (iki-daore), which means to drop dead on the street. Tokyo is so crowded and so busy, that you do sort of feeling like dropping to the ground in exhaustion sometimes. ^_^