We're working to make all our data (digital collections, catalog, branch information, etc.) as open, easy, and publicly accessible as possible.
Are there any APIs that you'd like to see?
PS: You can check out our Digital Collections API at: http://api.repo.nypl.org/
And, of course, our website at: http://www.nypl.org/
But WorldCat says there are only 10,136 items.
So, what data do you have that isn't already in there, and can you get it in there? Most developers I know that care about libraries are querying WorldCat.
Work with the Internet Archive to get your data included into https://openlibrary.org/
Once that work has been done, you can put your own API on the same data to address use-cases WorldCat and OpenLibrary don't (or don't easily).
Show movement: trends, patterns (like popularity, emerging popularity, new acquisitions)
Analytics for what data set? What media?
I suggest that you post the API page using the URL you mentioned, then add your question as a first comment in that thread. Good luck!