Here is an unusually good article on historic Italian libraries, published recently in the New York Times. It has to do with ancient libraries seen from the perspective of the tourist (albeit cultivated) and not the scholar. As shown in the piece, these libraries are not just about books and manuscripts but also about beautiful art and architecture.
Despite being a trained librarian and mega book lover, I myself neglected this aspect in my twenty years in Italy. I passed by the Marciana in Venice many times and never went in. This is mostly due to the forbidding nature of many of these places, which are carefully guarded and not tourist-friendly. Which is understandable, to a certain extent.
If you go, make sure to prepare beforehand and confirm rules for access.
