I've never referred to myself as an "American", I'm a New Yorker - everywhere I've ever traveled to (England, the Netherlands, Japan, Ireland, Canada, the Caribbean, Mexico, other states in the USA, etc, everyone knew what I meant when I said "New York". And if someone called me "American" I would clarify (not correct necessarily, but definitely clarify) "actually a New Yorker" because honestly while me and a person from California, or Oregon, or Iowa might all be from the same official country, we are from vastly different places and cultures.