The Nagasaki City Library is a very nice, very NEW library. They have a nice amount of fiction and non-fiction books on various genres. (The books on the shelves looked kind of like what I have at home...which I thought was interesting, and a tad bit disturbing...)
They do need more English books on Nagasaki and Japan but of course, if you can read Japanese, there's tons of books to read on the history of Nagasaki.
When I visited in December 2008, I spent about an hour or so reading about the REAL inspiration for Madame Butterfly...Tsuru Glover - the wife of Thomas Glover (from Scotland), one of the few foreign business men in Japan in the later 1800s. Their former residence is also a wonderful place to visit while in Nagasaki.
I can't say it enough...Nagasaki is an often overlooked place...please visit if you are ever in Kyushu!