While I appreciate the idea of staying somewhere for 3 nights, and not doing one-night stands, your plan to stay three nights in Kilkenny appears to be mostly using Kilkenny just for a launching pad for doing day trips, and not spending time in Kilkenny itself. If you haven’t already booked your lodging there, and don’t have other reasons for sleeping in Kilkenny for 3 straight nights, I’d change the 3-night plan.
Until this past spring, I’d never been to Cork, but thoroughly enjoyed our stay. Having lunch at, and touring the English Market was a fantastic experience. The Crawford Art Gallery is a manageable size (not huge), and even the Butter Museum is a worthwhile visit. If you’re going to Doolin for the traditional Irish music, Cork has many places to hear it, too. The great Blarney Castle, and its wonderful garden grounds, were easy to reach just outside Cork. Dinner at Goldie was very special. Saying in Cork would be rewarding, if even for just one night.
An hour northwest of Cork is the charming town Macroom, if you wanted to stay closer to Kilkenny at the end of Day 3 than if you stayed in Cork, and it’s close enough to the Ring of Kerry that you could use it to start off Day 4. Just west of Killarney is Ross Castle, well worth the guided tour they offer. After your Ring of Kerry drive, stay in Killarney at the end of Day 4 (just one night, since you have other places to see on your current agenda), and see Ross Castle late that day, or early on Day 5.
OK, so thoughts on Day 5. If you want to see some of the Dingle Peninsula, don’t do it as a day trip, then return to Killarney. Stay in Dingle. Or, failing that, pop into the Dingle Peninsula, stay as long as possible, then spend the night in Tralee before you head farther north on Day 6.
On Day 7, definitely do a walk to see the Cliffs of Moher from way up. I’ve seen them from a ferry coming from Inisheer, and they’re big, but they were more magnificent for me from the visitor center and a walk from there. I love Galway. At the risk of doing another one-night stay like much of what you’re already planning, go to Galway, and stay there at the end of Day 7. We stayed at the Petra House B&B. Have dinner at Oscars Seafood Bistro. The Galway City museum is worth a visit, and it’s free! Strolling downtown, and pubs around John F. Kennedy park are other highlights.