This is the oldest layer of Dublin, the patch the medieval walls once enclosed, walked in a slow loop from the castle to the two cathedrals that face each other across the high ground. Do it in the morning, museum doors opening, before Patrick Street fills.
Start in the upper yard of Dublin Castle — seven hundred years of British administration handed over in a single room in 1922 — then slip behind it to the Chester Beatty Library, free and quietly one of the best small museums anywhere, an hour of illuminated manuscripts and jade books. Up the rise, Christ Church and its enormous medieval crypt, mummified cat and all. Outside Dublinia, a real stretch of the old city wall still stands.
Down Patrick Street to St Patrick's Cathedral, where Swift was dean and lies under the floor, and next door to Marsh's Library, 1707, the oldest public library in the country, with its lock-in reading cages still in place. From there the Four Courts Luas is a walk north along the river, the medieval city behind you.