I was in Florida last week for a friend's wedding and took advantage of the services of the Franklin County Public Library Eastpoint branch to check in on my online class. They provide public Internet access to anyone, regardless of residency, which came in very handy. No forms or anything to fill out, just sign in with your first name and you're ready to go.
The branch is located in a shopping center just before the bridge to St. George's Island so I'm sure they get a lot of business. It had a very cool used book store feel with lots of shelves of books crammed into the relatively small space.
They also have this cool van which I think serves as their bookmobile. Or at least promotes library programs. A friend of mine saw it at Piggly Wiggly!
Another great beach library is the Tybee Island Library on Tybee Island, GA. They provide temporary borrowing cards to visitors and even have fishing poles and tackle available to check out! Any other favorites out there?