Well, I've checked the NY library - Cleveland has a much more extensive collection (I think e-books only are around 8,800 volumes, audiobooks are separate and I'm guessing around 4,000). Getting a card is restricted to permanent Ohio residents or people in Ohio for 6 weeks or longer -
http://www.cpl.org/index.php?q=node/34.
Maybe some out of state folks can e-mail to them suggesting something like NY - fee based for out of state (which should make sense, they shouldn't care if they are funded by property taxes or other fees).