There are various methods. You can fly. You could get a train. You can go by road, via the M7 and M8 motorways. You can go in a car or any of the many bus services that go between Dublin and Cork. Cork is a large county, so there are various parts of it to go to, and so there could be various routes when you get closer to your actual destination.
Kilkenny to Dublin.
Dublin and Cork are the names of cities and counties in Ireland.
You would need to get at least 2 trains, one from Belfast to Dublin and one from Dublin to Cork. They are at different stations, so you would have to travel from one to the other on arriving in Dublin, which you can also do by rail. The whole journey from Belfast to Cork could take between 5 and 6 hours, depending on the times you travel and the connections for the departure times.
to visit Blarney for the day you could travel by car on the M7 and M8 motorway - about 2.5 hours from the limit of Dublin or you could travel by train from Dublin Heuston to Cork and travel to Blarney from the station - about 3.5 hours
There is a motorway between Cork and Dublin, using the M8 and then the M7.
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The distance etween Dublin and Cork City is 160 miles. HOWEVER, the distance to County Cork (which is what I think you actually mean) from Dublin is 125 miles.
You would need to get at least 2 trains, one from Newry to Dublin and one from Dublin to Cork. They are at different stations, so you would have to travel from one to the other on arriving in Dublin, which you can also do by rail. The whole journey from Newry to Cork could take between 5 and 6 hours, depending on the times you travel and the connections for the departure times.
From Dublin you could get to Cork by road, rail or air. Having got to Cork, you can then get a bus to Dunmanway.
Dublin and Cork.
There are no postal codes in Ireland. Dublin does have some postal districts, and there is a Dublin 4, but no Cork 4.
The county of Mayo is much bigger than the county of Dublin. Mayo is the third largest county in Ireland and Dublin is the third smallest county in Ireland. The city of Dublin is larger than the town of Mayo.