Neloth in Dragonborn mentions that Telvanni has its holdings on Vvardenfell. This suggests Sadrith Mora is either the capitol or most prominent regional capitol of the house. The other major city is Telvannis, east of Sadrith Mora, which isn't featured in Morrowind but Tamriel Rebuilt built it(according to their mod, the archmagister of Telvannis is Rilvin Dral).
Neloth is currently in Tel Mithryn on Solstheim, having left Sadrith Mora before the Red Year. Who took over Tel Naga while he was gone?
Tel Uvirith is in northern Molag Amur and Baladas Demnevanni lives in Gnisis, both of those places would have been covered in ash in the Red Year. Telvanni Canton in Vivec was hit by the meteor, it is gone.
The current status of Tel Fyr is unknown, we could write new lore. Just as a heads up, afaik Divayth Fyr IS featured in Wheels of Lull which is a pretty popular quest mod. I don't know if you plan to tie in with that or not but I'm just throwing that out there. Should Tel Fyr be in the game as it was in Morrowind? It wouldn't be surprising if Divayth moved it into another dimension or something to avoid the ashfall.
Tel Aruhn(and Sadrith Mora) are out to sea a ways, they would likely have not been destroyed by the ash but would still have been effected by it. Gothren was killed by Nerevarine so Tel Aruhn would have a new wizard lord.
What would have become of Vos? What would Aryon or Dratha have done to protect it from the ash? How effective would it have been?
Tel Branora is well out to sea in the opposite direction of the main ash plume, so perhaps Therana is still alive.
So all in all the Telvanni will have been effected badly by the ash(except for Tel Branora), but not destroyed. New wizards will be ruling Tel Naga and Tel Aruhn, probably mouths or apprentices from the previous game or wizards from the mainland(that Tamriel Rebuilt has named, if you consider that to be fanon). Aryon and Demnevanni(if he survived) are the likely candidates for Archmagister, if we aren't going to factor in mainland newcomers. And Fyr will regardless of all other factors have done something completely wacky and extraterrestrial by his own accord, knowing him.