I'm not sure the first person's criticism is entirely fair, although in some places it is. For example, our flight from the US arrived around 7 a.m. on our first morning in Dublin. We were eating breakfast by 9 a.m., and did indeed have two full days, only staying two nights. And then Galway is only about a 2 hour drive from Dublin, so if you left at 8 or 9 a.m., you'd have two full days there too. In any event, there are lots of great sites all over Ireland, outside of the towns in which you plan to stay. For example, on the way from Dublin to Galway, you could stop in Tullamore or Clonmacnoise. From Galway to Limerick or Dingle (see below), drive through the Burren and stop at the Cliffs of Moher. From Dingle/Kenmare, stop at the Rock of Cashel. So my point is that even when you have long driving trips (and some of these will be), you won't be wasting your time. Just plan things to do along your route - there is always something good to see/do.
I would skip Limerick unless you have a reason for going there. It doesn't have the best reputation. Considering spending two nights in Dingle, it was our favorite place in Ireland, and I think many on this forum would agree. In my opinion, Dingle has the best pub/music scene in Ireland.
I would stay two nights in Kilkenny over two nights in Wexford. Nothing against Wexford, but Kilkenny has an interesting castle, a great old town, pub scene, and is more conveniently located.