So much underutilized potential on Azys Lla. Flew around there for a few hours just exploring, since there's so much you miss in your rush to stop Pope Thordan. The Habisphere, the Quarantine Block, the Mobile Supply Cache, the Pappus Tree... I wish I could learn more about them.
As for the "Anti-Tower," assuming it's on Azys Lla (which, despite my desire to have it be some part of Ishgard's Foundation, is the most likely case), I'd wager it's behind the red door on the back of the Flagship. The three doors ringing the Warring Triad are probably all entrances to the Aetherochemical Research Facility, so where exactly the entrance to the Holding Bay where we fight Sephirot (and likely the other members of the Triad is) remains a big question. Looking forward to it!
(Hopefully it's not quite as dull as Pharos HM and Saint Mocainne's were to me...)
Apropos of Sephirot, the reason his arena appears to have some plants and such around it is probably because he was worshiped by ent-like beings? The Sightseeing Log for the Cathedral on Azys Lla says he was worshiped by "treelike beings who believed themselves to be "remnants" of Sephirot." Aside from the obvious VII:AC reference, that explains a bit about Sephirot himself.