I've played D&D forever, but mostly in homebrew settings; I've never delved into the lore of the published settings. But now I'm playing in an Adventurers League game set in the Forgotten Realms, and I've made a character with the Archaeologist background.
One of the suggested bonds for this background is "I hope to bring prestige to a library, a museum, or a university." This fits my character idea, and a university makes sense to me, so I went to cast around for some established location that makes sense. I found a list of Educational buildings in the Realms, but it's pretty short — and it seems to be almost entirely wizard or bardic colleges, with a smattering of military academies.
Is there normal higher education in Faerûn? I mean a school (college, whatever) which might teach things like archaeology — or philosophy, history, rhetoric, math or whatever else is setting-appropriate (which clearly archaeologist is), but not as part of wizardly education or whatever. I know there are institutions with religious acolytes and arcane acolytes, but are there… undergrads, grad students, post-docs? (If not, where do archaeologists learn their trade?)
Is it reasonable to just assume that any big city would have a university or college or similar? I'd love to tie in to a specific place, because that's the whole point of this "bonds" thing.
Best Answer
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.