I know that I can use
hreflang for country specific content in order to avoid duplicate content, but what about city or state specific content?
Is that possible, and if not, how do I deal with it?
rel="alternate" hreflang="x" annotations cannot be used to specify a city, or any other geographical content other than the Language and region:
I doubt it ever will either, as it doesn't really make sense to have duplicate content on your city specific pages, Google would want you to make them unique. You should make your city specific pages unique to that city, adding some info about the city and write about your location in that city. (e.g, if you were a franchise store, write about that particulars stores history)