Go through the Monaghan County Museum and find the Cross of Clogher

Walk the Diamond and Market Square in the middle of the town

Find the Rossmore Memorial, the Victorian drinking fountain on the Diamond

Drive the drumlin roads out of town and see how the hills dictate where the road goes

Monaghan town is built around the Diamond and Market Square, in a county of nothing but drumlins — small rounded glacial hills packed so close together the roads have to wander between them. The county museum here opened in 1974 as the first full-time, professionally staffed, local-authority-funded museum in Ireland, and it won the Council of Europe Museum Prize in 1980; its collection runs from the Cross of Clogher to the linen and lace the county lived on.

Monaghan Town: The Cross of Clogher and the Drumlin County

Walk the Castle Trail to the ruins of Rossmore Castle

Walk the yew avenue from the walled garden

Find the wedge tomb and the court tomb in the park

Count the drumlins you can see from the high ground

Monaghan is drumlin country, a county of small rounded glacial hills, and Rossmore Forest Park, 320 hectares of woodland just south of Monaghan town, runs over and between them. It was the demesne of the Barons Rossmore. Their castle, built in the Gothic style in 1827 by William Vitruvius Morrison, kept growing: a rivalry with the Shirleys of Lough Fea over who had the largest room in the county saw the drawing room extended five times, and the house ended up with three towers and more than 117 windows in at least 53 sizes and shapes. The family left in the 1940s and it was demolished in the 1970s. An avenue of yews runs about half a kilometre from the walled garden, and the park also holds a wedge tomb, a court tomb and Californian redwoods.

Rossmore: A Vanished Castle in the Drumlins

Walk the single estate street of the village and see why it wins Tidy Towns

Walk down to the green lake the village is named for

Walk the Castle Leslie demesne on the edge of the village

Cycle the three kilometres to the border and back

Glaslough means green lake, and the village is a single street of estate housing three kilometres from the border, laid out beside the lake on the edge of the Castle Leslie demesne. It won the Irish Tidy Towns Competition in 1978 and again in 2019, forty-one years apart, which tells you something about how seriously the place takes itself. The lake is what the name says it is on the right day.

Glaslough: The Green Lake Village

Walk the drumlin lanes and lake shore around Annaghmakerrig — the Centre itself is a private working retreat, not a public house

Find out what Guthrie's will actually required of the state that inherited it

Look up which writers and composers have worked here since 1981

Tyrone Guthrie launched the Stratford Festival in Canada as its first artistic director and founded the Guthrie Theater in Minneapolis, and he died at his family's house at Annaghmakerrig outside Newbliss on 15 May 1971. The house became the Tyrone Guthrie Centre, a place where writers, composers and painters come to stay and are left alone to work — which is a rarer kind of legacy than a theatre with your name on it. It is a working retreat on a private estate rather than a house to wander into, and the drumlin country around it is the quietest part of Monaghan.

Annaghmakerrig: The House Tyrone Guthrie Left to Artists

Find the round tower and the Augustinian abbey ruins in the town

Stand at the Cross Moyle high cross in the middle of the Diamond

Find the stone sarcophagus said to hold St Tighernach

Look for the pictographic tombstones in the old graveyard

St Tighernach founded a monastery at Clones in the 6th century and his cult spread right across the British Isles. What is left is scattered through an ordinary market town: a round tower, the ruins of an Augustinian abbey, pictographic tombstones, and a carved stone sarcophagus said to be Tighernach's own. In the middle of the Diamond, the town square, stands the Cross Moyle high cross — five metres of sandstone, assembled from the parts of more than one cross.

Clones: The Round Tower, the High Cross and the Sarcophagus

Walk the shoreline trails through the old Blayney demesne

Bring your own kayak or canoe — there is no hire on site — and get out among the islands

Walk out onto one of the peninsulas and see how the drumlins shape the lake

Fish for pike or bream on Monaghan's largest lake

Lough Muckno is the largest lake in Monaghan and the town of Castleblayney sits directly above its western shore. The old Blayney demesne around it is now a public forest park of woodland, islands, inlets and shoreline, and enough water for rowing, angling and paddling. It is drumlin country, so the lake is a complicated shape with peninsulas and bays running in every direction.

Lough Muckno: Monaghan's Biggest Lake

Walk the great circular earthwork on the hilltop and pace out its size

Stand on the mound raised over the burnt timber temple

Find out at the visitor centre why a building would be made only to be burnt and buried

Go into Armagh city, the ecclesiastical capital that replaced Emain Macha

Emain Macha was one of the great royal sites of pre-Christian Gaelic Ireland and the capital of the Ulaidh, the people who gave Ulster its name — the seat of Conchobar mac Nessa and the Red Branch in the Ulster Cycle. What archaeology found is stranger than the legend. Around 95 BC a huge roundhouse-like timber structure, likened to a temple, was built on the hilltop, then deliberately filled with stones, burnt down and buried under earth to make the mound that stands there now. Nobody is certain why.

Navan Fort: Emain Macha, Capital of the Ulaidh

Walk right round the burnt-out shell and count the different shapes of tower

Go through both of the interconnecting walled gardens behind the house

Find out what is known about the fire of April 1933 — the cause was never established, and the inside of the shell is not accessible

Look at how much Gothic detail survives on a ruin nobody has restored

From the mid-1820s the English architect Thomas Cobden rebuilt Duckett's Grove for John Dawson Duckett in castellated Gothic revival, piling on towers and turrets — round, square and octagonal — until the house looked like several castles arguing with each other. It burned overnight on 20 April 1933 and was never rebuilt. The shell still stands, and the two interconnecting walled gardens behind it are run by the county council as a public park, free to walk into.