As you ponder how to find Hraesvelgr, you find help from an unexpected source.
This quest is available if you have completed the quest Mourn in Passing.
Starting the Quest
Talk to Alphinaud to begin the quest. There will be a cutscene.
Speak with Alphinaud
Attune to the Churning Mists Aetheryte if you have not already done so, then go southeast through the archway between the two fluffy white lights. Talk to Alphinaud to proceed.
Search for the Moogle
Go east to the orange circle on the map. There are two Aetheric Disturbances and three Destinations. You can ignore the Aetheric Disturbances (or check on them if you wish to see some optional text), then go to the northeast of the orange circle and check the Destination near Ysayle, go to the southeast of the orange circle and check the Destination near Estinien, then go up the ramp to check the Destination near the middle of the orange circle.
Report to Alphinaud
Go to the quest icon on the map and talk to Alphinaud to complete the quest.
Next Main Scenario Quest
After you complete the quest, you will need to be at least level 54 to proceed to the next quest. After you reach level 54, talk to Alphinaud to accept the next quest: Mountaintop Diplopmacy. There will be a cutscene. This one is important, so it is recommended to watch it either now or via the Unending Journey in an inn room.