Whenever people introduce themselves online I tend to see things like "I'm from London, England" from Englishmen, "I'm from Barcelona, Spain" from Spaniards, and "I'm from Florida" from Americans.
EDIT: Or an acronym, which is even more confusing for foreigners.
I've sort of run into this, but I think it's more of a famous-city thing than an American thing. At least in my experience, when I'm talking to Americans from Chicago, Seattle, San Francisco, Houston, Washington D.C., etc. they'll usually mention the city instead of the state, and they (as well as Londoners and Barcelonans) will assume you know what country they're from.
When I'm talking to Europeans who
aren't from large cities and are instead from, say, Ramsgate or Cadaqués, I'll get the same answer I get from someone in small-town America: "I'm from [country]. What city? Oh, you've probably never heard of it. Fine, it's [city]. Yeah, I thought so. No, it's nowhere near [famous city], not even close. Yes, I get that a lot."