Hello fellow Ireland travelers. I was in Ireland last spring, on an escorted tour. I am just sorry we didn't spend more time in Dublin. If your time permits can arrange transportation, I highly recommend a trip to the city of Waterford and a tour of the Waterford Crystal factory. That was incredible! The city dates back to the 800's, and is very charming. A second recommendation, again if you can arrange transportation, is the small town of Blarney, home of the Blarney Castle. Yes, it is a tour stop and you'll encounter a flood of tourists, but the Blarney Woolen Mill complex is full of Irish products -- a shoppers haven!
It's hard to say what is the most "must see" place in Ireland, it was all very beautiful (Ring of Kerry tour was a highlight). Do see a pub - they're everywhere! Very much Irish!
Have a wonderful time!