Following other library accounts is a great way to generate new ideas for your own Instagram account.
Below is a list of libraries who have demonstrated exceptional use of Instagram to promote the library and engage with users.
In no particular order,
San Francisco Public Library : https://www.instagram.com/sfpubliclibrary/
Los Angeles Public Library: https://www.instagram.com/lapubliclibrary/
Great Valley High School Library: https://www.instagram.com/gvhslibrary/
Buena Park Library: https://www.instagram.com/buenaparklibrary/
Des Moines Public Library: https://www.instagram.com/desmoineslibrary/
Madison Public Library: https://www.instagram.com/madisonpubliclibrary/
Cherry Hill Public Library: https://www.instagram.com/chplnj/
Additionally, you can find more libraries by using Instagram's search bar and typing "public library" or using the hashtag "#publiclibrary".