I am crazy about libraries and always have been. I guess I am an academic at heart--I tell my grandchildren that I stayed in school for so long that they made me the teacher. This topic has my head spinning in so many directions, that I don't know where to start.
First, I want to recommend The Library Book by Susan Orleans. While it is mostly focused on events at the Los Angeles public library, it does a nice job on the history of libraries in the US including how they are evolving today. It is also a kind of detective story about the fire that destroyed much of the main branch collection in 1986.
When I was a teenager, I spent a lot of time at the downtown main branch of the Los Angeles Public Library. They had an excellent collection of sheet music, and I was able to check out all sorts of chamber music ranging from violin-piano and trio sonatas all the way up to the Bach Brandenburg Concertos. These were not just scores, but all of the individual instrumental parts! This was the early 1960s, and in those days we did not have access to recordings of every imaginable work, so we discovered a lot by combing the music stacks, bringing home the sheet music, and playing it. That library also extended my exposure to music from Gregorian chants to John Cage. Just looking at the evolution of notation was an education in itself.