Familiar Faces is a main scenario quest though, and you can't abandon main scenario quests sadly.

I think the OP is actually confused about where he needs to go - it is not Azys Lla he needs for that quest at all, but the Sea of Clouds - specifically the island chain in the north west where Ok'Zundu is located called 'the Blue Window' (Azys Lla is a completely different zone). When Cid first dropped you off it should have been mentioned that an airship route between there and Ishgard was now established, so there should be an npc at the Airship Dock in the Pillars that will fly you there - as you're were trying to get to the wrong area it's entirely possible the airship route npc is there but you just didn't notice it.

Look for an npc there dressed in Garlond Ironworks attire and if he offers to fly you to the Blue Window, it's the right place.