I too use the public libraries - with cards at three different ones. The availability of new releases is all over the map. "Scarecrow" by Michael Connelly and "Hold Tight" by Harlan Coben were available at the library within a couple of weeks of being available at Amazon. But other things just never show up, and library offerings are truly library specific. Since I'm a Kindle user, I have to go through the conversion process, but after a couple of times, it takes seconds to do.
Some of the biggest library collections are New York City library (although they have stopped selling non-resident cards), Cleveland Library and the King County Library mentioned above. You can go to the overdrive site:
http://search.overdrive.com/ and search for any book or author and they will show which libraries carry it. Maybe this can give you a more conclusive answer for the books you like.
cheers