Many Irish itineraries begin in Dublin. If you have young children, the Dublin Zoo (one of the oldest in the world) is a fantastic stop. Beer aficionados should check out the Guiness Storehouse. Those of Irish heritage shouldn't miss "The Famine Memorial". Other attractions of note include Dublin Castle, John's Lane Augustinian Church (Catholic), Trinity College, St. Patrick's Cathedral (Anglican), St. Mary's Pro-Cathedral (Catholic), and, if the children need some time to run around, Phoenix Park.
The Dingle Peninsula is your next stop. Consider a kayak tour of Dingle Bay or a boat tour to see the famous "Fungie the Dolphin". On your way to Newmarket-on-Fergus, stop at the tiny town of Blennerville to see the working windmill.
Dromoland Castle near Newmarket-on-Fergus is a perfect base to explore the surrounding area. The Cliffs of Moher are a must see attraction and kids of all ages enjoy the demonstrations at the Burren Birds of Prey Center.
Northwest of Newmarket-on-Fergus, you'll find spiritual and historic sites including Croagh Patrick (tradition tells us this is the mountain where St. Patrick spent Lent in 441) , Kylemore Abbey and the Shrine of Knock.
On your way back to Dublin (or as a side trip before you fly out of Shannon), take a slight detour to visit Clonmacnoise, the ancient monastery. It is a beautiful and reflective last stop to end your tour of the Emerald Isle.