Which one is grammatically correct "Jack has never been to America" or "Jack has never gone to America"
Generally, the difference between been to America and gone to America is that the first implies and has come back and the second doesn't.
(This is a special meaning of been - it doesn't work with any other form of be, so you can't say I want to be to America.)
However, in this case, the never neutralises the difference. As Kate Bunting says in a comment, been is more idiomatic, but both are grammatical, and in this case have no practical difference in meaning.