In the case of the The World-Eater's Eyrie quest, Aranea Ienith will not come back to Azura's Shrine. Any other followers will also not come back to their original locations. They will simply wait for you until you leave the location of the The World-Eater's Eyrie and the succeeding quests (same behaviour as if you went to a dungeon or location where your follower cannot follow you, like the Dark Brotherhood sanctuary) - they'll follow you again automatically after leaving that dungeon or location.
Once you've finished the main quest,
you will find yourself in High Hrothgar with your current follower.
No need to go back to the location where you hired your follower (Azura's Shrine, in Aranea Ienith's case).