Find the octagonal lavabo, the washing house, the best surviving piece of the abbey

Walk the chapter house and trace the outline of the precinct

Stand where the Treaty of Mellifont was agreed with Hugh O'Neill in 1603

Work out what changed in Irish monasticism when the Cistercians arrived in 1142

An Mhainistir Mhór — the big monastery. Malachy, Archbishop of Armagh, founded Mellifont in 1142 to bring continental monasticism into Ireland, and it was the first Cistercian abbey in the country, and most of the others were founded from it. What survives is the octagonal lavabo where the monks washed before eating, the chapter house, and the outline of a very large precinct. It was dissolved in 1539 and turned into a fortified house — and in 1603 the Treaty of Mellifont, which ended the Nine Years' War, was signed in its grounds by Hugh O'Neill.

Mellifont: Ireland's First Cistercian Abbey

Walk right round the kerbstones of the mound — Dowth is free and unticketed, unlike Newgrange and Knowth

Find the crater left in the top of the mound by the 1847 excavation

Find the third entrance on the west side, an early Christian souterrain

Look for the quartz fallen outside the kerb, from the white facing the tomb once had

Stand outside at the winter solstice, when the alignment is on the setting sun rather than the rising one

Dowth is the third of the great Brú na Bóinne tombs and the one almost nobody visits — which is the reason to go. It has never been independently dated, but its features put it with the others, between roughly 3200 and 2900 BC. Quartz found fallen outside the kerb suggests it too was faced in glittering white stone. Dowth South, the shorter of its two passages, is aligned on the winter solstice sunset rather than sunrise, so the low light runs along the left side of the passage and lights three stones in the chamber. And on top there is a large crater, left by a botched Royal Irish Academy excavation in 1847 and never repaired.

Dowth: The Third Tomb, and the Crater in It

Find Muiredach's High Cross at Monasterboice, 5.5 metres tall and regarded as the finest high cross in Ireland, beside a 28-metre round tower

Walk the ruins of Mellifont Abbey, Ireland's first Cistercian abbey, founded in 1142 on the orders of St Malachy

Visit the Battle of the Boyne Visitor Centre at Oldbridge, where William III defeated James II on 1 July 1690

Compare Monasterboice's round tower with Mellifont's Cistercian ruins, a few kilometres and several centuries apart

The Boyne Valley did not stop being important when the passage tombs were built. Muiredach's High Cross at Monasterboice stands 5.5 metres high and is generally reckoned the finest high cross in Ireland, beside a round tower of 28 metres. A few kilometres away, Mellifont was the first Cistercian abbey in the country, founded in 1142 at the instigation of St Malachy to bring continental monasticism to Ireland. And at Oldbridge on 1 July 1690, William III beat James II on the river and settled who would wear the English crown.

Monasterboice, Mellifont and the Battle of the Boyne

Start at the Brú na Bóinne visitor centre and take the shuttle across the Boyne

Go into Newgrange and stand in the chamber the solstice sun reaches

Find the carved entrance stone at Newgrange

Walk round Knowth and its 17 satellite tombs, and look at the kerbstone art

The bend of the Boyne holds at least ninety monuments — passage tombs, burial mounds, standing stones and enclosures — and has been a World Heritage Site since 1993. The passage tombs were built from about 3300 BC; Newgrange, from around 3100 BC, is older than Stonehenge and the Egyptian pyramids, faced with white quartz and ringed by carved kerbstones, and at the winter solstice the rising sun shines through a roofbox and floods its chamber. Knowth, a little older, has two passages and 17 smaller tombs around it, and the largest assemblage of megalithic art in Europe. There is no direct access: visitors go by shuttle bus from the Brú na Bóinne visitor centre, on guided tours only.

Brú na Bóinne: Newgrange and Knowth

Climb the Hill of Slane and pick out the Hill of Tara 16km to the south

Walk the ruins of the 16th-century friary and college on the summit

Climb the friary tower for the view over the Boyne valley

Work out why a story about a fire needed these two hills to be inter-visible

Muirchú, writing a heavily mythologised Life of Patrick in the seventh century, says that Patrick lit a Paschal fire on this hilltop in 433, in direct defiance of the High King Lóegaire, who had forbidden any fire while the festival fire burned on Tara. Historians think Muirchú moved a fire lit somewhere else to Slane for the sake of the story — and the reason the story works at all is that you can see Tara from here, sixteen kilometres away. The hilltop now carries a ruined 16th-century friary and college.

The Hill of Slane: The Fire That Was Not Allowed

Climb Millmount and go into the Martello tower shelled in the Civil War in 1922

Go through the Millmount Museum below the fort

Find the preserved head of St Oliver Plunkett in St Peter's Church

Walk the Boyne quays and find where Cromwell breached the walls from the south in September 1649

Stand under St Laurence's Gate — the twin-towered barbican that guarded the east gate, which has itself vanished

Drogheda, the largest town in the Republic, has more history packed into it than most Irish cities and gets a fraction of the visitors. Millmount stands on a great mound on the south bank of the Boyne and has been the town's strong point since the Normans — through Cromwell's assault in 1649 and on to 1922, when its Martello tower was shelled almost to pieces in the Civil War. Across the river in St Peter's, the preserved head of Oliver Plunkett has lain since 29 June 1921: Archbishop of Armagh, hanged at Tyburn in 1681 as the last victim of the Popish Plot, beatified in 1920 and canonised in 1975, the first new Irish saint in almost seven hundred years.

Drogheda: Millmount, the Siege and a Saint's Head

Climb the three-storey tower house and find the trefoil-headed windows

Find the high cross in St Fechin's graveyard and the Crucifixion carved on it

Walk down to the coast at Seapoint from the village

Work out how many tower houses like this once stood along the Pale

Tearmann Feichín means Féchín's church land, and the village keeps two things from very different centuries in it. In the graveyard of St Fechin's there is a high cross carved with the Crucifixion. And a few hundred metres away stands a tower house of the 15th or 16th century, three storeys with good trefoil-headed windows — a small fortified house of the sort that once stood all over the Pale, most of which are gone.

Termonfeckin: A Tower House and a High Cross

Walk out to Cromwell's Castle, Cromwellian in origin from 1653 and rebuilt as a gun position in the Napoleonic wars, still standing over the Shannon crossing

Find the Salt Battery — Fort Eliza — with its emplacements for four cannons, and the Martello tower

Walk the harbour and the marina on the Shannon

Find Charlotte's Way, the house once called Hill House, where Charlotte Brontë's widower lived out his life, and the house Trollope lodged in

Banagher sits on one of the very few crossings of the mid-Shannon, and it is fortified out of all proportion to its size. Cromwell's Castle, built in 1653, still stands controlling the river; so do the Salt Battery — Fort Eliza — with emplacements for four cannons, Fort Falkland, and a 19th-century Martello tower, all of them put there to hold one bridge. Anthony Trollope lived here in the 1840s, and Arthur Bell Nicholls came back to Banagher after the death of his wife Charlotte Brontë and lived at Hill House until 1906.