Library Lion by Michelle Knudsen and illustrated by Kevin Hawkes is a lovely story set in a library:
Miss Merriweather, the head librarian, is very particular about rules in the library. No running allowed. And you must be quiet. But when a lion comes to the library one day, no one is sure what to do. There aren't any rules about lions in the library. And, as it turns out, this lion seems very well suited to library visiting. His big feet are quiet on the library floor. He makes a comfy backrest for the children at story hour. And he never roars in the library, at least not anymore. But when something terrible happens, the lion quickly comes to the rescue in the only way he knows how.
Needless to say this book always reminds me of the fabulous New York Public Library: