Lightning Hairstyle

[Sagittarian]

I was actually just about to ask about this.

The aesthetician, I read about the quest and saw the hilarious cutscene from it. But, as a noob, how do I even get to where the quest is?

If you didn't start in Limsa, you need to get to level 15 and advance the storyline enough to get the airship pass.
If you really want, you CAN run from Gridania, through Ul'dah, to Vesper Bay and catch a ferry to Limsa there.