Think about your priorities -- because you are going to need to make painful choices. Though Ireland may look small on a map, there is a lot to see and do, great things are scattered all around the country, and it takes a bit longer to get around than many people expect (yes, it's Europe, but don't expect the signature European efficiency when it comes to zipping from place to place quickly).
First step: start by being honest with yourself: how many full, non-travel days do your really have, on the ground, once you have arrived in Ireland? Hint: what many people call "a 10 day trip" only gives them as few as 8 or 7 full, usable days. That's not enough to get all around Ireland and see everything, of course. So think about your priorities, your tastes, and what might be on the top of your list of "must-see" places.