To see the cultural core of a nation that truly puts its literary heritage at the heart of its identity, you need only go to Trinity College Dublin and visit Trinity College Library. This houses the Book of Kells, one of the country’s most significant cultural treasures, but is also a cultural treasure in its own right, with its stunning two-storey Old Library.
The Book of Kells exhibit itself is, if not exactly tourist cliche, rather what you would expect. Since the Book itself is too precious to expose more than a couple of original pages at any one time, it is supported by a plethora of audiovisual displays on the context and period of the Book’s creation c.800 AD, as well as other relics of the period and of the tradition of Insular illumination. (You can see the whole Book in Trinity College’s digital archive here.) The Book is also supported by a very comprehensive souvenir and gift shop on the way out of the Library.
For me, the Library itself is the real goal for a visitor. The Old Library, the masterpiece of Irish architect Thomas Burgh, was completed in 1732. In the 18th century it was gifted with the Brian Boru Harp, one of the three oldest surviving medieval Gaelic harps, and the model for the harp in the Irish coat of arms – and on every Guinness label. It is Ireland’s only copyright library to hold copyright deposit rights for the entire British Isles. Its alcoves are interspersed with busts of famous figures of learning, including Jonathan Swift. As well as its superb collection of other manuscripts and bibliographical treasures, it displays a copy of the 1916 Proclamation of the Irish Republic.
Google Arts and Culture has an entire section devoted to Trinity College Library, which you can view here.