The New York public library uses Instagram to let clients know of current and upcoming event. At the top of their page is a link to their website, so if you see a photo and want to know more information you just have to click on the link. They also have a shop in the library and they can advertise all their products on Instagram.
their Instagram address is @nypl
Closer to home, the Yarra Plenty Library have lots of photos on their page showing clients in the library, in action, reading! Great promotion for people to get down to their local library.
check them out on Instagram