Mo Mowlam's vision for Stormont was for the acres of ground to serve families and the wider public. At first glance the extensive white house on the hill, flanked by rows of ancient trees, doesn't look open to anyone apart from broadcasters with a hard-news agenda. On closer inspection, however, a memorial stone to the former Secretary of State for Northern Ireland and a play-park in her name suggest her hopes for this green space were realised.

Young families chomp sandwiches round picnic tables and the waft of a late summer barbecue indicate that one of Belfast's best-kept secrets is out. The bucolic beauty of the estate is featured in two long woodland walks and it's not long before you forget about the obvious associations with the mansion on the hill.

My first night is spent in the four-star Stormont Hotel, which serves its purpose well. Throughout Northern Ireland there is a cottage industry built around the history of one of its most lauded sons, Van Morrison. Tour guides have already organised Morrison-themed trips to Bangor following the release of Going Down to Bangor on his latest album, Keep Me Singing, and the Van Morrison Trail takes in locations such as his childhood home and Cyprus Avenue, the other-worldly tree-lined street immortalised in the song of the same name.

Taking something of an alternative Van-related option I meet with self-confessed Vanorak Al Bodkin, a former RAF officer who served in tours of Kosovo, Oman and Iraq. His company Irish Heartbeat offers trips around Vanland in East Belfast but I opt for the road trip less travelled. Beforehand I head out to the leafy suburbs and Shandon Park Golf Club for a live performance by Celtic Soul, a tribute act with a difference in that they embrace more of the poetic aspect of the singer's career while taking the audience on a more colloquial journey peppered with anecdotes about the man, his work and the places that inspired him. Musically they summon the lauded early 1970s period, running through songs Morrison is perhaps less likely to play these days.

Setting off early the next day on a bright autumnal morning we are joined by local folk singer Rhiannah Warm for the Coney Island tour. The spoken-word track from Morrison's 1989 album Avalon Sunset and its related sojourn attracts tourists from around the world, and as Bodkin suggests it can be a disparate cluster, from "high-rolling New York lawyers and musicians" to Stormont ministers.

Our day out in South Down begins with a play of Liam Neeson's atmospheric version of Coney Island, and we soon take in the stunning Mountains of Mourne which are said to have been the inspiration for CS Lewis's Narnia.

The first stop-off is Shrigley, a village that sprang up around cotton-mill production, although all that remains is a clock tower and a fountain out of place and time. Next, Killyleagh is home to Ireland's oldest inhabited castle, surviving Cromwell's invasion and an IRA ambush. On a Sunday morning there's not a soul to be seen but this soon changes further down the road at Downpatrick Cathedral, which draws in busloads of pilgrims arriving to see the grave of St Patrick and a gnarled Celtic Cross at the front of the cathedral grounds. Whether he is buried here or not is another matter but that doesn't deter the throng.

Our Ulster trail continues to Ardglass where the culinary part of the excursion allows us to sample the potted herrings which Morrison chronicled himself munching "in case we get famished before dinner". The vinegary silver darlings are perhaps associated with another era but they are an active presence on the taste buds, evoking the ordinary moments of pleasure documented in the song.

Coney Island is more than childhood reminiscences of seaside trips for the songwriter – Morrison would undoubtedly have enjoyed the connection with Lawrence Ferlinghetti's collection of Beat poetry, A Coney Island of the Mind. Morrison's father is also said to have owned a small house on the island.

A weathered, rusty sign informs us that we have reached our destination. The morning sun has long vanished making way for intermittent drizzle which begins to drift down as we walk by a row of fishermen's cottages, now somewhat refurbished for modern life but still releasing the evocative smell of a coal fire. Some brave swimmers race past a marooned vessel from the rough, overgrown wilderness and splash into the water.

At St John's Point stands the tallest lighthouse on the Irish coast, reaching up 130ft (40m). This is where Morrison stopped to do some bird-watching while informing us that "the craic was good". It's not bad today either and Rhiannah is not shy in offering a song or some accompanying percussion. Al shares some of his own near-death experiences of life during the Troubles and proves to be an entertaining and informative guide. As we head back towards East Belfast, our final stop is for ice-cream at Fusco's, the parlour Morrison references in his song On Hyndford Street. It's unclear whether it's exactly the same establishment in which Morrison satisfied his sweet tooth at but the sundae tastes good all the same.

In the late afternoon it's time for a gear change after meeting my wife from George Best Belfast City Airport. We loosen the purse strings and hire a chauffeur-driven car for another journey off the beaten track, this time to the Glens of Antrim and the village of Ballygally. The drive to an ancient fortress – the 17th-century Ballygally Castle – takes around 40 minutes. It's not long before you are in the back of coastal beyond looking out over the hills and far away. You can gaze across to Kintyre on a clear day by the golden sands of the beach opposite the castle, built by a Scot, James Shaw, in 1625. The glens have a very Scottish feel and you can see why the makers of Game of Thrones chose this setting.

Twin red velvet chairs in the Ballygally lobby make the most of the Game of Thrones connection – the cast and crew stayed at the castle during filming – and the hotel also features the ninth of 10 wood-carved doors dotted around Northern Ireland that are inspired by the HBO series. The door leads to the hotel's Garden Restaurant and sirloin steak proves to be a highlight among the local produce on offer.

The castle is also allegedly one of the most haunted places in Ulster, a spiral staircase leading to the former room where resident Lady Isabella Shaw jumped to her death.

An Ulster fry sets us up for our last full day before heading back into Belfast. Our final stop is the Culloden, whose name honours the stone which was transported from across the water in 1876 and used in its construction. A roaring fire greets guests along with staff dressed in Victorian finery. Most rooms have a view of the gardens, which look out on to the Belfast Lough. Morrison sporadically performs here and our last night offers a rare opportunity to see him sing close to where it all began. Tonight he performs to around 300 fans during an intimate dinner-and-show event. Celebrating Northern Ireland's Year of Food and Drink the hotel's awardwinning kitchen offers a locally sourced three-course meal starting with a Portavogie fishcake, slow-cooked Irish beef for the main and Bewley's coffee and vanilla panna cotta to finish. At our table locals and tourists mix well, many having travelled far and at great expense for the experience.

The hotel manager invites a selection of requests for popular songs and Morrison seems to thrive in the environment. Among the fans Judy, a retired teacher from the United States, explains her reasons for the trip. "There are not many opportunities to see someone of his stature in a setting like this," she says. "For me it's the way he writes about women – I think there's an understanding. That and the fact he still has the voice."

Travel notes

Getting there

Flybe has daily return flights from Glasgow to Belfast from £53 and from Edinburgh from £56. Visit flybe.com.

Where to stay

Rooms at Stormont Hotel cost from £125 per night, at Ballygally Castle from £130 and at the Culloden from £180. Visit hastingshotels.com.

What to do

The Coney Island tour is run by Irish Heartbeat Tours. Find them on Facebook or call 07807 015403.

For Chauffeur Car Services, near Belfast, call 028 9336 7899 or 07968 246538.