The National Library has a wonderful W. B. Yeats exhibit in the basement. And the restrooms are something to write home about!

Katie, you can go to the National Library and see if you are related to the Cronin's of Dublin.

Thank you for all of the suggestions! I made a preliminary itinerary for when my family arrives. My family is only there for a quick week and traveling for two of the days. They don't want to be driving too much. Here's what we came up with.

Fly into Shannon arrive Saturday morning.
2 nights (Saturday/Sunday) - Galway
2 nights (Monday/Tuesday) - Cork
2 nights (Wednesday/Thursday) - Dublin
Fly out of Dublin Friday

OR

Fly into Shannon arrive Saturday morning.
2 nights (Saturday/Sunday) - Galway
2 nights (Monday/Tuesday) - Kilkenny
2 nights (Wednesday/Thursday) - Dublin
Fly out of Dublin Friday

I'd personally prefer to go to Cork, but my family does not want to drive TOO much. Is the drive from Galway to Cork worth the trip? Is there lots to do in Kilkenny? Thanks for all of your help thus far.

Whether you do Cork or Kilkenny I would only have one night and use the other night to split Galway and that point. It depends on what your group do want to see and do. Also you will have done Cork in the first week.
This thread has got somewhat confused and I'm not sure that I haven't answered the same on another forum. and I thought the Ring of Kerry was a must see?

Yeah - It's a little confusing planning a trip with two different groups. Ring of Kerry was a must see but that has changed. If we had to pick between Cork and Kilkenny, which should we choose?