How does Google maintain/update the information for the GeoCoding API?

The good news is that you can do it for NYC using OpenAddresses data. We published two pieces about how to geocode more generally:

https://www.nettoolkit.com/geo/the-basics-of-geocoding https://www.nettoolkit.com/geo/adventures-in-address-parsing

It turns out that geocoding has been a much bigger project than we anticipated, but we offer the service very inexpensively. Let me know if you have any questions.