This is a great idea. I can imagine it being implemented in the many slum communities in the developing world, which do not have access to electricity or water most of the day and that are open to ideas that could make their lives easier. It is a very self-sustainable model and could impact the lives of many people in developing-world mega-cities. Would be very happy to see this actualized :)!
I really like this idea- bravo! It would not only bring a community together, but it would push forth a consensus on the importance of renewable energy and would make a whole community (as opposed to only certain wealthier or more informed individuals) flourish. I would love to see a prototype sketch of this community center you envision. Perhaps the renewable-source logistics (which ones to incorporate) could be tweaked according to the environment/culture.
Let's say your product is viable and you have the best team around to make your hydro-power idea implementable. Have you thought about how to go about pitching this idea to policy-makers? How would you convince them that your idea is the most cost-effective and sustainable and worthy of investment? Why would they invest millions of dollars in this project when there are other imminent city issues to take care of? I am sure you are just brainstorming and have not moved on to the prototyping stage, but the issues of implementation are always the least thought of but are usually the most important in elevating an idea to reality (mass scale and utilization by the public).
I recommend doing some research in this respect on a city you could picture as your initial testing ground.