The National Gallery and National Museum are two separate entities close together in the center of Dublin 2. There are several branches of the National Museum but the Archaeology Branch is closest to the National Gallery and definitely worth a stop if you’re visiting the area.
The National Gallery contains a collection of works from Irish artists as well as other exhibits. While small, the Irish Art collection is impressive in its range of genres and techniques. Be prepared for crowds since tour upon tour dump their human contents into this space. Allow at least 45 minutes for the Irish Art section.
The National Museum, Archaeology is the place to visit if you want to see millions (literally) of artifacts found on Irish soil. Its an impressive collection as a whole but the spotlight for me was the collection of gold objects; the workmanship is commendable even by modern standards. Allow a minimum of 2 hours just for the major exhibits.