Greetings. I would recommend you investigate how the US Census Bureau handles geography. In fact, they already have a comprehensive coding for State/County/Place for the entire US, including areas not covered by all levels of geography - like Native American land, islands, etc. A good place to start is their Guide to State and Local Geography:
You can find links to hierarchical diagrams, reference materials and other useful documents. You may find the article on ANSI codes of use:
There is even a download page if you want to import there geographical codes:
Working with a major municipal government which happens to fall within five separate counties, we run into these issues a lot.
I would also caution you about using ZIP codes, as they are not really geographic areas but rather collections of postal carrier routes. In fact, the Census Bureau disclaims this on their page dealing with postal codes. US Postal Service builds their ZIP routes solely on business needs and cross city, county, even state lines with a single ZIP code.
The DBA mantra should always be "know your data, know your data" so understanding these relationships is important before you make business decisions based upon them. ZIP codes were meant to facilitate mail delivery - that is all. For other types of business, particularly Public Safety (which we support) you need something different.
I hope that this is useful to you.