Having never lived in a major city like Tokyo, Yokohama, Osaka, or Kyoto, I'm not sure. 

I can say that even major cities have residential areas, and from what I know about some of the surrounding suburbs of Tokyo like Saitama, the small neighborhood cooperation with shared responsibilities still exists. 

In areas that are mostly condos and apartment buildings, things change slightly, but even some apartment buildings have community rooms and meetings where issues are discussed and people either volunteer to or are appointed to lead morning exercises for the children during summer vacation, etc. 

A lot of this attitude is developed in Japanese schools. The ideas of working together, joining clubs or groups (in university and afterward they often call them circles) is very common. So I think that, though the community aspect may not be as localized as it is in smaller towns and cities, it still exists in the form of social groups. In addition, regarding these festivals, larger festivals are often joined by companies, which means that all of the employees will participate as a group and you will find the community aspect expressed through job loyalty and company pride, etc.