Firstly it should be a public building.
The promise of john Rocque's map of Dublin showing a seamless connection between the public domain and the interior. Also it would allow the space in front to be properly designed as a pedestrian space. And no no squares, leave the street as a street. Perhaps we could also get the "square" in front of the GPO removed as well and return O'Connell Street to a street.
As a public building perhaps there are too many museums though a proper Dublin Civic Museum would be appropriate since the building was the important link between the city and the country and the island and Britain.
It should also have a temporary exhibition space for important visiting expeditions including previewing major projects and ideas.
An alternative perhaps it could be a science museum and look instead to the future.