Juliejames had several good suggestions. Here are a few other options.
For a full day from Kilkenny, you could drive around the countryside to visit Kells Priory and the Kilree Round Tower and High Cross (8th/9th century) then visit Jerpoint Abbey. They are about a 30 minutes drive from Kilkenny. From there, you could continue on to Waterford (about 45 minutes from Jerpoint Abbey. Waterford has several museums, especially Viking related exhibits. Waterford isn’t a great night life town, so you could head back to Kilkenny for the evening (good restaurants and pubs).
Wexford is another nearby city (about 1.5 hours drive) with several options, including visiting Tintern Abbey or trying an outdoor adventure with sea kayaking
http://theirishexperience.com/
I enjoyed Kilkenny, but 4 nights might be a bit much if you want to see other parts of Ireland. You might devote 2 nights to Kilkenny and consider spending a night or two in Killarney or Kenmare and visiting the Rock of Cashel on your drive from Kilkenny there. While in either town, you can see several sites in the area and drive the Ring of Kerry for vistas of the Irish Coast.
If you want to see the Cliffs of Moher, they are over 3 hours drive from Kilkenny, so you may want to spend a night somewhere near the Cliffs instead of driving back to Kilkenny. Ennis and Doolin are nearby (pubs and music). Galway is about 1.5 hours.
Hope you enjoy your stay
Raymond