If we were starting from scratch I would advise neighborhoods to create your own governments (Neighborhood Governance) and then delegate to the next level of government only that which truly cannot be done in the neighborhood. If you can do something it will be done better--more effectively--which in the long run is more efficient, period.
Starting from where we are today, I would advise neighborhoods to find ways to Solve Problems that are too vexing for municipal governments, and ask that in exchange for taking care of one of their headaches, the government return some authority to the neighborhoods. It would be nice to get them to return some of your tax dollars but don't hold your breath. The goal here is to create a better place and way to live through hyper local decision making, problem solving, and innovation. Living with necessarily insensitive decisions made outside your neighborhood should not be acceptable. That said, and repeating myself, you will still have to create value for municipal government for them to return some of your autonomy (self-governance).