The Book of Kells
First thing in the morning, they walked quite a few blocks to Trinity College to see the famous Book of Kells. The line was quite long.
Entrance to the college:

Imagine our surprise when, just as we were looking at a map of the campus to see where to go for the Book of Kells, Katie the Hitchhiker bops up to the same map! We had not seen her since we dropped her off in Charlestown, just before we headed into Northern Ireland.

In addition to the Book of Kells, Trinity College Library has a long, tall hall where they have collected many, many old books.

An even better exhibit is the Chester Beatty Library and Galleries, which include illuminated manuscripts (like the Book of Kells) as well as treasures from the Orient and Middle East, and older documents including some of the oldest extant fragments of the Gospels, on papyrus.