Answer:
No, Shakespeare is not known ever to have travelled out of England, although he might possibly have done. His early life was in and around Stratford-on-Avon, most of his life writing and performing drama was in London. In any case, he didn't have to go to Italy to get the tale of Romeo and Juliet since it was readily available in England in Arthur Brooke's English poem Romeus and Juliet (which is exactly where Shakespeare did get it).