When he found the site in 1998, he was young, and the building was for sale.
"As I travelled back to London the idea of buying it kept surfacing," Conway says.
However, as he became immersed in his career at the London Chest Hospital, the idea fell by the wayside.
"A year later I was back for good in Kilkenny. At the auctioneers I noticed the for sale leaflet with 'sold' stamped on it. My heart sank."
But by a stroke of good luck, the Chamber of Commerce wasn't able to muster the funds to buy the bar and the auctioneer told him to come back the next day, which he did.
Conway then spent 10 years painstakingly restoring the site, which was originally the inner house of a Tudor-era mansion built in 1582 by the future Mayor of Kilkenny, Martin Archer, then a member of a powerful merchant family.
A hole was punctured in the rear wall of the building in the 1700s to gain access from the High St, leading to the establishment's name.
Amazingly, the 1582 fireplace, oak lintels, oak beams, two Tudor-cut stone windows and original plaster had survived the ravages of time, Conway says.
The Hole in the Wall then became the Hole in his Pocket - the restoration was exorbitant and occurred during the peak of the Celtic Tiger economic boom, he says.
"Everything had to be done as a conservation project."
Expensive engineers, conservation architects and heritage experts on dendrology, lime plaster, stone masonry were required by the Heritage Council, Conway says.
"The costs have been such that other home projects have suffered and a certain car is on blocks."
Since its rebirth, Conway has been drawing patrons in with live and, due to the size of the Hole in the Wall (more than 20 people is a squeeze), intimate music sessions and SingSpiel shows - a German-derived format of storytelling that incorporates, but is not limited to song, poetry, props and video.
Recent iterations have included shows about Antarctic exploration and local mining history.
And outside of regaling wayward tourists who stumble upon his hidden bar? Conway continues to work at a cardiologist at the local St Luke's hospital.
GETTING THERE
Air New Zealand offers daily flights from Auckland to London via LA, with onward connections to Dublin on partner airlines. One-way Economy fares start from $1539. airnewzealand.co.nz
ONLINE
holeinthewall.pub
ireland.com.