favourite definition comes from The Devil's Dictionary by Ambrose Bierce: "A saint is a dead sinner, revised and edited." The stories, legends, myths and traditions associated with Saint Patrick are a case in point. We know very little about Patrick of Ireland; we can't even say for sure where he was born. But his story lives on, sometimes as a religious tradition, sometimes as a political tradition, and sometimes as both.
Whether he came from England, Scotland or Wales, we do know that Saint Patrick wasn't from Ireland. This 5th century Roman Briton was apparently abducted at the age of 16 and brought to Ireland by slave-traders. Six years later, he escaped back to the larger island to the right of us, then returned as a missionary priest some years after that. If there are no snakes in Ireland it is because of the Ice Age, rather than Patrick's episcopal crook. But the influence of Christianity on this island, which this legendary figure has come to embody and symbolise, has been immense. Few of Patrick's writings have survived, but we do have two documents, his Confession and his Letter to the Soldiers of Coroticus, which give us a sense of the person behind the legend
We remember him today in Ireland because March 17 is thought to be the day on which he died sometime after AD 460 (ish). His grave is reputed to be outside Down Cathedral in Downpatrick -- which certainly sounds like the place where the saint was laid down to his rest. Down's claim is not undisputed, however Another tradition has it that St. Patrick ended his days in England and was buried in Glastonbury. The Chapel of St. Patrick still exists as part of Glastonbury Abbey.
I'm not a betting man, but if I was, my money would be on Wales as the birthplace of Patrick. As for his burial site, your guess is as good as mine; but I'm not prepared to challenge the claim of Down Cathedral.
Incidentally, as this image shows, Patrick is also venerated within the Orthodox Communion, with many examples of icons celebrating his life and work. Ireland, north and south, is now an ethnically diverse island. Patrick should be hailed as the patron saint of the New Irish. He is still our most famous immigrant.