The earliest reference I can find to surface drow settlement is Buiyrandyn which was founded by Eilistraee worshippers sometime around 747 DR. I'm guessing that because the Seven Sisters were born around that time and the youngest of the lot, Qilue, would have died due to her mother being killed in childbirth (their father thought she was possessed by an evil spirit) resulting in Mystra acting quick to save the unborn soul. Around that time Illiryztara Veladorn had suffered a miscarriage in traveling to the location of Buiyrandyn and it was likely to result in her death as well since (I'm guessing at the time Eilistraee didn't have the power to just save her). Mystra worked out a quick deal with Eilistraee and Qilue's soul was bound into Illiryztara allowing her to born and saving her....second mother's life....?
Magic and gods is weird, y'all.
Anyway, I'm not sure if this is when Buiryandyn was being founded or if it had existed already and Illiryztara was simply making her way there.
Buiyrandyn was later destroyed by mind flayers.
Anyway. Eilistraee had a powerful cleric in Qilue and contacts as well via her half-elven sisters (The aforementioned Seven Sisters.) who tended to be Harpers, were Chosen of Mystra (Qilue is also Chosen of Mystra despite following Eilistraee), and having several major positions. This helped give non-evil Drow a reliable support network to start building.
By the time Drizzt Do'Urden came to Icewind Dale in 1347 there were several permanent and semi-permanent Eilistraee settlements in secret here and there as well as a handful of drow worshippers of human gods. Drizzt just somehow never managed to find them in stumbling over the surface.
*shrug* - maybe most of them were clustered in the Heartlands... I don't know.
Liriel Baenre found all sorts of surface drow in the same time period...though she was actively looking for them, now that I think about it. Liriel ended up a cleric of Mystra and living in Rashemen accepted as one of the Witches of that culture...I think...haven't finished that series yet.
Between the 1300s and the 1400s the surface drow grew progressively more public. Around the Second Sundering (1480) Corellon granted many of Eilistraee's worshippers a reprieve from the curse given to the Drow when they allied with demons and chose to serve Lloth (Drow itself as a word means something like "traitor"). This reverted them to looking more like their pre-curse state (which is still dark greys and dusky colors).
In 1374 drow still provoke immediate fear when they first meet people, much more so than tieflings who provoke suspicion and are sometimes treated as easy targets. However, drow can fairly easily convince people they're not evil. (reference NWN2 when you rescue Neeshka. If the PC is a drow, the guards and Neeshka will be initially terrified or when you meet the merchant in the starter village, he begins terrified of you.)
In my opinion, mechanically speaking, most of Eilistraee worshippers that have been surface-dwelling for generations should be statted as wood elves and/or high elves. (Similar to how High Elves in Faerun are split between Sun Elves and Moon Elves) And calling them drow seems wrong, because again, that means traitor, but they do share a lot of cultural similarities with drow because they do accept a lot converts.
But. Eilistraee's followers don't frequent major cities too much. They tend to dwell in hidden areas or close to openings to the Underdark or other dangerous locales because giving aid to the lost and hopeless is a major part of their philosophies.
However, Eilistraee's followers aren't the only large group non-Lloth following drow around. There's also the Vhaerun drow who are....basically capitalists. Vhaerun is as much an enemy of Lloth as Eilistraee is, though he's more motivated by selfish desires and hate than concern for his mortal elven kin. Vhaerun drow tend to be shady merchants (lots of hooks into smuggling, piracy, and human trafficking...though some are just actually legitimate merchants who tend to undercut people) as well as mercenaries. Most famous is the mercenary company of Bregan D'aerthe. To make a Star Trek comparison, think Ferengi philosophies, but Cardassian social graces. They're very similar to the modern Zhentarim, actually.
While most of my encounters in-game with Bregan D'aerthe are further north (Waterdeep and Luskan, specifically)...they're a pretty broad company (they've appeared in and around Amn in some novels). They are also not the only group of Vhaerun worshippers. And while Baldur's Gate (the city) doesn't have much in the way of attraction for Eilistraee worshippers, it is a thriving market place for Vhaerun worshippers.
Also note that the PC and other characters likely weren't captured in Baldur's Gate. So they could have been anywhere.
Also, the "Seldarine" drow still uses the same dialogue tags as Lloth-sworn...so they feel more like they're Dark Seladrine than Seldarine right now....
I'm assuming for now that Seldarine drow are mostly recent converts/escapees from Lloth-sworn societies (hopefully they'll give us Vhaerun as a worship option eventually.)
As to the "Dark Seldarine" other than Vhaerun (Eilistraee is fully accepted in the Seldarine at this point I think) they're mostly either not that interesting...Selvetarm actually manages to be less narratively interesting than Lloth...mostly because he's a Lloth-loyal fanatic that doesn't appear to have much more thought than a hungry gnoll…..or not very well organized like Kiaranslee and Ghaunadaur…
To tell the truth though, Kiaranslee might be interesting (drow goddess of undead, necromancy, and vengeance)
Anyway...that's the situation. 1480s surface drow still get side-eye but they aren't so unusual anymore.