If based in Belfast, it is only around 1-1.5 hours driving to reach the Hoo, Ireland's only caving hut and a palace fit for kings. The Hoo is within walking distance of Marble Arch Caves and less than 15 minutes drive from other classic caves on Cuilcagh mountain (Prods Pot-Cascades Rising, Shannon Cave, Tullyhona and more). Noons and Pollaraftra are two other classic caves a bit further of a drive away and quite a few smaller caves exist in the Fermanagh-Cavan area.
Dublin is where the majority of cavers in Ireland live, aside from those down in Clare and up in Belfast. There are people caving in Fermanagh from Dublin at least once a month, generally more. They mostly do tourist caving, but if you are looking to do some exploration then members of the Shannon Group are the people to ask, there are still a few kicking around though activity has slowed quite a bit since the mid-late 2000s when they were pretty active.