A prime example of a recurring FF staple that really should be in the game! An mmo library can also be continually updated with more books, have quests revolving around it, and be a hub for many other content (newspapers, gaming tournaments, etc)
FF wiki Library
Pasted the images here from the wiki (I added in FF3 and FF6), and I'm pretty sure there are libraries from more games not listed here:

FFIII - Grand Library in Saronia

FFIV - Eidolon Library

FFV - Library of the Ancients

FFVI - Figaro Castle Library

FFVII - Shinra Mansion Library

FFVIII - Balamb Garden Library

FFIX - Alexandria Castle Library

FFIX - Daguerreo Library

FFTactics A2 - School Library

FF Crystal Chronicles