The National Association for Education Statistics has a site where you can search for libraries by state or town or zip code. (Please note these are public libraries only. Also, you'll need to make appropriate choices in the "Library Types" box.) The nice thing about this directory is that it often has circulation numbers along with detailed contact information.
National Association for Education Statistics:
Library Search
Here is what the American Library Association says:
"A directory of all libraries in the United States does not exist. The closest approximation of such a publication is the American Library Directory 2004-2005."...
..."Individual library entries in the American Library Directory provide names of staff and contact information, with the library's address, phone number, fax number, and web site address and e-mail address, if applicable, as well as information about the library's finances, population served, and holdings."
(source: ALA Library factsheet)
You can also check the American Library Directory. You need a subscription to access it regularly, but there is a free 14-day trial period that might work well for you.
A nice thing about the American Library Directory is that you can search on library type, address (state), holdings, etc. and even download results.
Another good site to find all kinds of information about libraries is the Open Directory Project.
From their site:
"The Open Directory Project is the largest, most comprehensive human-edited directory of the Web. It is constructed and maintained by a vast, global community of volunteer editors."
Right now you can find links to 26 different kinds of library directories, as well as Friends of Libraries sites, special library information, etc.