Help! How Do I Find the Entrance to "Lady of the Vortex" on the Map?

[Enkidoh]

Kirika's answer is obviously 100% what you need. I just felt that i would add that i think the NPC Enkidoh was remembering was in Gridania, not Ul Dah. Its been a number of years since i did this as well, but in my head we set out from Gridania rather then Ul Dah on this particular mission.

Doh! You are totally right Frizze, I remember now - I got mixed up between the aftermath of the escape from Castrum Centri and the departure to fight Garuda, the former of which the Enterprise docked in Ul'dah, however it's Gridania where the Ironworks npc would logically be, given Gridania is physically closer to the Howling Eye (which is somewhere near the border of the Black Shroud and Coerthas) than Ul'dah, so I am so sorry for the mixup Grokus (my kitty memory is too muddled with catnip I think! haha ).

So yeah the Ironworks engineer that could fly you back to the entrance of the Howling Eye would be at the airship dock in Gridania downstairs from the Carline Canopy.

Anyway, thank you so much for clarifying that Frizze, I greatly appreciate it.