I want to build a database of geographical locations and would like to be able to identify locations that fall inside other locations. For example, The Empire State Building is going to have one geo-coordinate, but my database would be able to tell me that it falls inside Manhattan, which falls inside New York City, which is in the state of New York and so forth.

I've been looking at OpenStreetMap which seems to have a pretty decent database but as best I can tell, I would need to create a set of polygon structures representing each region and then detect if a coordinate falls inside a given region's polygon. Is there a better way to do this, or is there a data source where all of this has already been calculated?