We spent 2+ weeks in Ireland several years ago. We flew into Dublin and rented an apartment just off O'Connell St - we stayed at least 5 nights, and took a day trip to
Newgrange with Mary Gibbons.
We then went back to the airport to pick up a rental car (why is the airport NEVER in the direction we're traveling???). We basically used Rick Steves tour of Ireland as a general guide, except we stayed two nights in most places, ended our tour in Galway, and drove back across Ireland to spend our last night at a Dublin airport hotel. Between Galway and Dublin we stopped the Irish National Stud, which, as horse-loving Kentuckians we found fascinating.
We spent 3 nights in Galway and took a daytrip to the Cliffs of Mohr. We did RS drive north of Galway but ran out of time at the end of the day and din't get to visit Kylemore Abbey, which broke my heart. (We finally got back last near and I got to see all of Kylemore Abbey!)
We spluged on the Ring of Kerry and hired a RS recommended driver so that we could both sit back and enjoy the scenery. Take a look at some tours of Ireland to see where they go - and why. We skipped Waterford because all the info I read made parking seem like a nightmare, and neither the Titanic nor the crystal connection was important, so we just skipped it.
We did go back last year and traveled north from Dublin, thru Belfast, along the coast, then down to Galway and back to Dublin, so we completed our loop.