We spent three nights in Cork last May and spent one day on a day trip to Cobh where we took a walking tour (called Titanic Walk), and went to the Titanic Experience and the Queenstown Story. The walk was not really about the Titanic or we would have overdosed. The train trip was short and pleasant.
The second day was spent trying to follow the self-guided walks ( https://www.corkcity.ie/en/things-to-do/parks-outdoors/cork-city-walks/ ) which was made difficult by the many missing way markers. The English Market was interesting, and the Butter Museum was delightful.
All three nights included being at Sin é for great trad sessions beginning at 6:30pm. Get there early for a good seat and don't sit in the corner booth in the back (or you'll get bounced by the musicians). Cork City subsidizes these sessions (http://www.theleesessions.com/index.php) and they move around on a weekly basis.
Depending on your flight times, you might have time to visit Bunratty Castle, the Hunt Museum and/or King John's Castle in Limerick, and Mallow Castle. There's also Blarney Castle and Gardens, although we've never been due to our dislike of crowds of tourists.