There are a number of ferry ports from which you can cross the Irish Sea. You can cross from Stranraer, Scotland to Belfast, Northern Ireland taking a scenic route thru Donegal, down through Mayo to Galway.
If you choose to cross the sea from Holyhead, Wales to Dublin it's a quicker run cross-country
Either way is a nice drive it all depends if you want to see/avoid Dublin.
The Island I think you were refering to are the Aran Islands. Achill Island is worth a visit if you find yourself in the vicinity