There is the national history museum on Merrion Square in Dublin, we had ds there when he was about 2 and he loved it.
It full of Animals and there is a huge whale hanging from the celing…. Im not sure if its open again as there was a big accident and one of the staircases collapsed during the summer… Im sure you will find something on line
When we went to dublin we got the open top tour bus, its hop on hop off system, so you can visit all the museums in one visit (National history, Killmainham, Collins barricks etc)