I'd translate this as : I'd like to visit places in America and Japan that I've never been to before.
This seems to be an answer to a previous query. As with many Japanese sentences, the "proper" translation is very dependant on the context.
行ったことのないアメリカ seems to me that the person has been to America before, but is talking about places in America that they haven't yet visited.
A literal translation might be "The America that I haven't visited"
As for #2, I don't have a perfect answer because I'm not a student of grammar, but there is a slight change of nuance between の and が here.
が makes it sound more like the person has never been to America at all.