I've actually watched a few anime in which America is portrayed, but the one that comes to my mind immediately is a show by the name of Baccano!. It is set in 1930's New York and Chicago and has a lot to do with the mob, which was very powerful at that time. For the most part, it looks like the writers and artists of the show did a lot of research. Buildings and slums look like they should, the popular clothing styles are represented quite well, but a a certain point caught me giggling slightly to myself. That is the widely popular portrayal of Americans as either reckless, trigger happy, dumb, or very friendly (through physical contact, pats on the back, handshakes, etc.). In Baccano! they are mostly very dumb and triggerhappy, this is pretty much wholly diguised by the violence required for the show, but there are some points when regular, ordinary people just pull out guns or knives and I can't help but feeling slightly like smacking my hand against my forehead.