The Feast of the Moon seems the closest. A summary from the Forgotten Realms wiki article:
The Feast of the Moon [...] was an annual festival occurring between the final night of Uktar and the first day of Nightal -- traditionally marking the onset of winter. It was also a time to celebrate and honor the ancestors and the respected dead. Folk blessed their ancestors' graves and performed the Ritual of Remembrance. People also gathered to tell stories of the deeds of their ancestors and of the gods until deep into the night, until they merged and become legend. This was a time to hear of past heroes,
great treasures, and lost cities.
In Faerûn, battles were typically fought between harvest-time and the coming of winter. This meant that most of the fighting usually occurred in the month of Uktar. The timing of the Feast of the Moon—after recently slain soldiers had joined the ranks of the dead—was thus practical, if sadly ironic.
In a magical medieval world like FR, I am not sure if it would be easy to find an institution of higher learning that is not connected to theology, military or magic. Even Earth's fair share of universities were founded with religious studies playing a core role.
As a concrete example, consider the so-called City of Splendors, Waterdeep, one of the largest cities in the continent of Faerun, and possibly the most influential. An entire 2e boxed set, and a 3.5e sourcebook was dedicated just to this city. The 3.5e sourcebook describes it to have over 130k population which increases 5-fold in the summer months. The city boasts 12 churches, 4 or 5 arcane schools, a large number of guilds, places to obtain poisons, potions, magical and mundane weapons, a great library associated with the church of Oghma, 11 independent sages (mostly mid-to-high level experts) specialising in various mundane and arcane topics, but only a single organization that is categorised as scholastic, the bardic college New Olamn. No universities at all.
If you decide to expand your question to allow temples and libraries in FR, then the list is a lot longer of course. The most famous of the libraries is Candlekeep. Another one would be the High Temple of Mystra on Mount Talath in Halruaa. Others can be found on the FR wikia. Furthermore, if you allow universities of magic, 3e FR Campaign Setting (FRCS) mentions that it is not uncommon to meet wizards who are university graduates in the lands of Lantan and Halruaa.
Finally, if you want to stick to universities and find the Zakharan and Oriental institutions listed in guildbounty's answer too far, you can try the Great University in Gheldaneth. To the extent that I know, that is the only university that is mentioned by name throughout the whole FRCS. (With its 320-pages full of two-column small-font text, FRCS is arguably the most information-dense sourcebook published on the Realms.) The Great University was one of the two most prominent buildings (the other is the Wizard College) of that metropolis, which happened to be the second largest city in Mulhorand, and ruled by clerics of Thoth. Unfortunately the city survived but got devastated by the Spellplague, so it is not clear what the current whereabouts of the university are.
There is good support that it probably means "shield" or "barrier" or "gate" or the like
I agree with Miles Bedinger's answer noting that dwarven words relating to "shield" start with "bar", and that this may be a clue to the semantics. To wit:
There are further considerations that support this conclusion. Based on various sources from earlier versions of D&D materials, these places were all originally established for the sake of their being defensible positions that controlled folks passing through to somewhere:
Incidentally, the surname "Barr" in English etymologically is related to "gate", and its meaning goes back to the Middle Ages when, like many old surnames, it represented one's profession; it was short for "Barrier" who was a "maker of bars," i.e., city gates. This may or may not be relevant to how the designers fashioned the dwarven language, but it's an interesting coincidence to say the least.