Handle location in a SQL database
Are you aware of the "what3words" system??  https://en.wikipedia.org/wiki/What3words

Or, how to address mail from the U.S. to anywhere in the world  - a problem similar to yours - https://blink.ucsd.edu/facilities/services/mail/international/addressing/index.html

I've seen geographical data represented with latitude/longitude or similar coordinates, plus a code representing how specific or accurate the coordinates are.

You could use coordinates together with a textual address.  The text is searchable but the coordinates -are-specific.

I think the proper way at the moment to store arbitrary text with markups for field identities - name of country / county / town etc. - is XML.  A similar effort of your own would be just re-inventing XML.

How does the Smithsonian do it?  Or is that where you're doing this?