Pretty sure its in Vesper Bay. Either the injured adventurer behind the Waking Sands, or the one out front who has given ones to you in the past. Either way, i'm certain Vesper Bay has the quest you need.

Edit: Checked the Wiki, You can access to this dungeon by speaking with a quest giver in Vesper Bay in Western Thanalan at level 35. The Name of the quest is Braving New Depths. It is the same quest giver that gives access to Halatali.-< from thge Wiki page.