There is no easy answer to this question, for most towns, even quite small ones, have libraries. They are regarded as a common cultural need. And some local authorities have a number of them. Queenstown Lakes District Council, where I live, has at least 7 of them. Not sure this is good enough. A cursory look at the public libraries website suggests an average of 50 per region over 8 regions suggesting a figure of around 400. A closer answer must be quite easily obtainable even though sometimes definitions are not exact. Quite a high number for the population but then it is mostly rural and many of the libraries I presume are very small.