Only have 2 days in Ireland. 1st will be in Dublin. Where would you spend your 2nd day that wouldn't take too long to get to.
Anita, will you have a car to travel from Dublin in, or will you depend on public transit? If it were me I'd just stay in Dublin, rent a car and do a day trip for the second day, perhaps up to Newgrange. You could also skip the car and take the train up to Belfast, Northern Ireland, for the day, or do a local "tour bus" day tour.
If you have a car, I'd suggest either Newgrange/Knowth or Gelndalough and Powerscourt. If you go to Newgrange, allow plenty of time, you may have to wait a bit to get a spot to shuttle over to the site. If time allows, the Hill of Tara is close to Newgrange, as are the Monasterboice round tower and high cross (they aren't worth a trip on their own, but make a nice add-on to a trip to Newgrange. If you don't have car, there are probably day trip tours to Newgrange from Dublin.