Here are some of the locations from "Faiths and Avatars" and "Powers and Pantheons". As someone pointed out, Oghma would would be a good place to start, so I figured I'd check there. Obviously, the great temples to various deities even aside from the gods of knowledge would hold libraries of information related to their gods' portfolios.
Deneir's entry lists the following:
Iron Dragon Mountain in the Earthfast range contains a place known as the Master's Library in Faerun. The most comprehensive library in the realms, exceeding even Candlekeep, the Library of Curna in the mountains of the same name, and the great libraries of Shou Lung. A group known as the High Librarians, powerful followers of Denier lead by Haliduth Orspriir (allegedly over 600 years of age) protect and maintain the place, along with allies that include dragons. Devout followers of Deneir are said to make a pilgrimage to the library, but most never make it past the Reading Room, a small hold south of the true temple.
Other important sites mentioned are Silverymoon in general, the Herald's Holdfast, the artifact Museums of Calimshan, Twilight Hall in Berdusk (the Harper center of power), and Soaring Spirit in the Snowflake Mountains.
Gond's entry lists the High Holy Crafthouse of Inspiration, a walled monestary in Lantan...there's also one in Tilverton, though presumably that's in the black void thingy and thus a moot point.
The Mystran Church maintains a library in a cavern complex in Mount Talath in Halruaa. But, it is apparently only open to Halruaans of the Mystran faith.
Oghma's entry mentions Candlekeep as the greatest learning complex in Faerun, which differentiates it in my mind from the above mentioned Master's Library. Entry to Candlekeep may seem to carry a steep price, but it has always in my mind seemed very...vital and alive, as opposed to just a storehouse.
The Leaves of Learning in Highmoon is apparently a recently prominent temple of Oghma. If I recall from the relevant Volo's guide, the high priest is pioneering something like a card catalogue and making accessing books in various temples a much quicker process. Other prominent temples are the Tower of Thought in Selgaunt, the Domes of Reason on Procampur. The newest Grand Temple (circa 1368 DR) is the Font of Knowledge in Waterdeep.
The Library of Curna, mentioned previously, is the center of Oghma's worship in the Shining South. In contrast to many of his libraries, which focus on histories, it concentrates on current events, business and naturalistic studies.
Savras has a temple in Tashluta called the House of the All-Seeing Orb which might be an excellent source for sages. It is listed as the home of over a thousand sages, the college of Divination, the Celestial Observatory and the Library of Ultimate Truth. If it were my campaign, I would make this place a great storehouse of prophecy.
Thoth, the Mulhorandi god associated with knowledge has a university known as the Arcanum of Magic in Gheldaneth. In addition, his priests rule the city, known in Mulhorand as a place where even slaves must learn to read, write, count and answer basic questions of Mulhorand's history. It is probably the greatest center of general knowledge in the Old Empires region
Now there's a good sampling, but these obviously don't include any kind of secular or private libraries. Many sages likely keep the only copies of their findings with them in the wilderness. There are numerous Royal Libraries or varients thereof, some of which I imagine would be administered by the Heralds. Certain organizations will of course have private libraries...for example, I seem to recall an organization of explorers in Suzail that keeps the journals of all its previous members.
Faerun does not lack for knowledge repositories. Hope this helps!
Good info nonetheless
