Sean,
I've gone on three hikes in Ireland.
I have a great recommendation: Croagh Patrick. I climbed it in 1997. Here is some background: http://www.croagh-patrick.com/visitorcentre/need-know. The mountain trail is unpaved and fairly rugged (and a even bit dicey in a few spots, but just a few).
Croagh Patrick is in northwest Ireland near a town called Westport in County Mayo. It's the holy mountain of Ireland. The story is St. Patrick prayed for the souls of the Irish on its summit for the biblical 40 days and 40 nights. He chose it for prayer because it had been used for pagan bonfires previously. There is a chapel on the summit. The mountain is only 2,500 feet high. I climbed it in 2.5 hours. The mountain almost perfectly conical. On a clear day, the views of Clew Bay are stunning. If you do this climb, make sure you see Rockfleet Castle on the opposite shore of Clew Bay.
I've also hiked two 100-mile long trails, including the Wicklow Way (http://www.wicklowway.com/) in eastern Ireland. It starts (or ends, depending on direction) from Dublin's Marlay Park, a city park. It's pretty rugged and unpaved. The best section is around Glendalough.
Also, I've hiked the Dingle Way (http://www.dingleway.com/) in southwestern Ireland. It's slightly better than the Wicklow Way, because of the drop-dead views of the Atlantic Ocean and Dingle Bay, but remote. It's mostly along unpaved paths. The best section is around Mount Brandon, which the trail crosses, on the north coast. The Dingle Way is packed with thousands of Irish antiquities. It's the real Celtic experience.
In addition to all this, I've heard good things about the Kerry Way (http://www.kerryway.com/), which is immediately south of Dingle on the Kerry Peninsula, and the Western Way (http://www.irishtrails.ie/Trail/Western-Way---Galway/37/).
Hope this helps. Cheers.