Need multiple tag "sets"

Hi to all!
I need for my website something like multiple tag “sets” (I don’t know what would be correct term for this), to be able to search independently. Example: I have “products” that should be tagged once with name of a city/town, and with the second tag set with the state name.
Prod1, tag1: Chicago, tag2: IL
Prod2, tag1: Brooklyn, tag2: NY
Prod3, tag1: Queens, tag2: NY
Prod4, tag1: Brooklyn, tag2: NY

So, selecting “Brooklyn” for tag1 will show all products related to the selected tag (in this case Prod2 and Prod4). Selecting “Chicago” for tag1 will show Prod1. Selecting “NY” for tag2 will show Prod2, Prod3 and Prod4. Etc.

If there is maybe better solution to do the same please let me know.

Thanks for any help.