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

[Enkidoh]

Primal fights are in the Duty Finder, but they're not dungeons, they're called 'Trial Battles', and so Garuda would be in the Duty Finder under 'Trial Battles ~ A Realm Reborn' and 'The Howling Eye'.

Otherwise, I'm pretty sure there should be a temporary npc at the Airship Dock in Ul'dah which should provide you access to the entrance to the Howling Eye if you speak to them (I think they may be an Ironworks employee), but the DF is the faster option (the npc would disappear after completing the main scenario quest it's a part of).