Kilmainham holds the two faces of Irish history side by side: the grandest classical building in the country, full of modern art, and a mile west the prison where the state was born in blood. The walk takes in both, with formal gardens and a war memorial folded in, and the Liffey to bring you home.
Start at the Royal Hospital Kilmainham, a 1684 home for old soldiers built around an arcaded courtyard on the model of Les Invalides — walk into the quadrangle before anything else. The building is now IMMA, the national modern-art museum, free and quietly excellent; the restored formal gardens on the north side are emptier still, and the best place to sit on the whole route.
West along the road stands Kilmainham Gaol, where the 1916 leaders were executed — the heaviest place in modern Ireland, and worth the walk even if the tour is full. Drop down to the Liffey for the War Memorial Gardens, Lutyens' sunken rose gardens for the Irish war dead, then follow the south bank back toward Heuston and the Luas.