Maybe something from history.
Or traditional costumes that people wear during holidays.
Maybe from the military, school, or government ceremonies.
The major ones I think of in the US are the square top caps that students wear when they graduate.
There’s also the baseball cap, famously worn around the world with New York Yankees or Los Angeles Dodgers logo.
I know the “cowboy hat” is worn in Texas but where I live, San Francisco, I only see Mexicans wear them. So I don’t think of them as “American cowboy hats” but as sombreros vaqueros lol