Best places to visit with public transport challenge

I'm bringing my Dutch girlfriend home for 10 days over Christmas and want to bring her to some nice places - BUT - neither of us drive since you don't need to in the Netherlands due to the amazing public transport.

Obviously Ireland is different and is in fact the 2nd most car dependent nation in Europe, so its more a thought exercise in how we have closed our nation off to those who don't drive.

I'm from Cork and looking at that as a jump off spot specifically, but you could share your hidden jewels from anywhere.

So where are the best places available to get to with public transport?

As in a train to a town, and then a bus to a megalithic tomb. Or a 3 hour bus from the city centre to an ancient monastery. Or a 2 hour drive to a seaside town with a round tower etc etc.

Is it possible? Would someone without a car be able to visit small, out of the way Irish historical sites?