We've provided some App Ideas to get you going, i.e. give you some ideas of community. They are located in the above folders. Some are open-sourced which generally means that the source code is available free of charge to the public to use, copy, modify, or distribute. You can try to adapt them to a more local community need. Others are presented to give ideas of the types of community based apps that are being developed. Finally, some are in the idea stage, and represent a need identified by a client.
Code for America Commons A source of up-to-date database of government and civic software -- both the apps themselves and where theyre used. Many of them are open sourced, but certainly a place to get ideas.
NYC BigApps 3.0 was an app development competition held in 2012. The submissions vary, but may give you some ideas.