Trinity College Library (the 'Long Room'), Dublin. There has been a library at the College ever since it was founded (in but the Long Room was not begun until Completed in it is the largest library in Ireland, containing books.
Next time I'm in NYC this is a definite stop! The Pierpont Morgan Library in NYC is one of the grandest libraries in the United States. It was designed by Charles McKim and built in 1906 to house the private library of financier J.