Christ Church Cathedral has a history going back to around 1030 AD under the Norse king of Dublin, Sitriuc Silkbeard. It's officially the seat of both the Church of Ireland (Anglican), but in practice that honor goes to St. Mary's since the English Reformation. It's still the cathedral of the Archbishop of Dublin, however.
Nearby St. Patrick's Cathedral, also Anglican, is the latest of several churches that have stood here since the fifth century AD. The lure of the site was a well that once existed here, where St. Patrick is said to have baptized converts to Christianity. The combined choirs of St. Patrick's and Christ Church Cathedrals sang the first performance of Handel's Messiah (although not in either cathedral). Because it's hemmed in by buildings, I wasn't able to get a good photograph of the exterior, but its well decorated with busts and shields.
One of a couple of Celtic gravestones dating from somewhere between the 7th and 10th centuries:
The Chapter Door, which commemorates the amicable conclusion of a feud between the Earl of Ormond and the Earl of Kildare in 1492. The former had taken refuge in the Chapter House and the latter cut a hole in the door and stuck his arm through to shake the hand of his former enemy in reconciliation. This is supposedly the origin of the expression "chancing your arm," meaning to take a risk.