re: 3 days in a Ireland

3 full days?
Get out of Dublin. You can stay in Dublin for ease of lugging luggage around but take day trips out of Dublin.
Plenty of bus tours that will take you to the Cliffs of Moher, Galway, Kilkenny, rock of Cashel.

I can expand upon those places but just get out of Dublin is my biggest suggestion. I've been 4 times, most recently in March, and less than 50 percent of the people I met in Dublin were Irish.
With that said, Dublin Prison, Irish whiskey museum and trinity college are accross the street from one another and are both quick and great. Jameson is a good tour and we did teeling this March and enjoyed it. Guinness is pretty cool but just takes a while.

Go find pubs that have traditional Irish music.

I've done car rental, busses, and train and they all have advantages but it depends on what interests you.

TLDR: daytrips out of Dublin, or take the train/bus/car to galway and spend a day around there/go to the Cliffs. Second day stay in Kilkenny. If renting a car stop and the rock of Cashel on the way. 3rd day spend in Dublin.