All Might is blond, and he uses an American-themed suit, and labels all his attacks with American city names.
At first, I thought he could be American, but then he has a Japanese name and works in Japan.
Is All Might Japanese, American, some other nationality, or is it unknown?
His full name is Toshinori Yagi which is a Japanese name as you said and according to wiki his birthplace is Tokyo.
Other evidences are:
His mentor, Nana Shimura, is also Japanese.
All Might also go to U.A. High School and his homeroom teacher was Gran Torino.