As I've mentioned, I work for a smallish (4,000 FTE) university in a medium-small town of about 17,000. As an academic library, we of course are part of the OCLC network, and interlibrary loans flow in and out of here daily. However, our town's awesome public library, which isn't part of any consortium or group, doesn't have the money for that, though they can and do loan and borrow through the state's ILL network. As a college town (and a surprisingly intellectual one for being in the middle of the bible belt), we have lots of retired professors who stayed on in the area, several authors who moved here for the rural setting (that's still within 45 minutes or so of the big city) and cheap cost of living, and plenty of avid readers.
Many of these folks don't have privileges at our library, don't use us often enough to justify purchasing our "community borrower" card ($20 for lifetime privileges), but still occasionally need something a bit more scholarly than they can easily access through the public library.
On the opposite side of the coin, we have lots of students who commute to school here but who don't live or work in this county (the requirement for a card at the public library), and that want to get a hold of a novel that we don't have in stock. (We do try to buy most of the bestsellers as well as particularly popular genres like Fantasy, but we can't get everything...) Enter our awesome serials librarian, Jan, who worked with the director and head of ILL at the public library to create a resource sharing agreement between the two libraries. In a nutshell here's the process.
1. if a patron at library A is looking for a book that library A doesn't have, they or the librarian can pull up the OPAC for library B and see if Library B has it.
2. If Library B has the item, Library A calls Library B, and the item is checked out in Library A's "name". Library A is responsible for keeping records of which patron has which book in case of problems, and will charge the patron to recoup any overdues/lost book fees that accrue.
3. The patron will be given a receipt at library A with the title of the book, which they present at the main desk of library B to pick up the book. When the patron is done with the book, it can be returned to either library (though we prefer library B, for obvious reasons).
The resource sharing scheme has been going for about 2 months as a "pilot program", and we plan to tinker with the system over the summer. Our two libraries are about 5 minutes apart, so it isn't a major hardship to get to library B to pickup. We've put up posters in both libraries explaining the system, and had a nice writeup in the local paper to coincide with the launch. I don't think either side expected this to be a huge source of business, but we're doing 2-3 transactions a week--and those who have done it like the system, so hopefully word of mouth will grow the program.
I know all of us academic librarians communicate well with each other (at least the ones who follow this blog do!), and I'm sure your director goes to lunch with your public library's director on occasion, maybe they even serve on each others' boards. That said, how strong is your library's relationship with your local public library? Go over and introduce yourself to your counterpart, volunteer, offer to do a bit of training on Library 2.0 "stuff", or even work together on a joint outreach project like our resource sharing scheme. There is a lot of overlap between the users of the public library and academic library, and by working together we can support each other, strengthen our presence(s) in the community, and create plenty of win-win situations.
