If Sika is a potential guest for the Ember Court, this quest will show up on your world map as a blue ! marker. In beta, it only shows up after you fly to Bastion.
Fly to Aspirant's Rest. Sika is at /way 52.68 82.59, in Aspirant's Crucible. She wants you to talk to various people in the area and help arrange to have her duties covered so she can take time off for your party.
Ikaran, Sophone, and Leda are all nearby. Adonas is just outside the village at /way 52.57 78.11, surrounded by aggressive Starved Etherwyrms. Fight them off, then click Adonas to bandage him.
When you return to Sika and turn in the quest, don't forget to use the RSVP item so she comes to your party. Sika prefers a [spell=336512] court.