Mention to pals that you're going to the Millard Fillmore Presidential Library, and you can tell they're impressed by your intellectual curiosity. Then they figure out it's a dive bar with craft beer in burgeoning Collinwood, and they're even more impressed. Fillmore was the USA's 13th president, and from New York incidentally. But that shouldn't hinder a great bar name.
There is indeed a 'library' and it consists of four books at the end of the bar; ask the friendly bartender to point it out.