Honorhall Orphanage is located in the city of Riften. It was there that young Aventus Aretino was sent after the death of his parents. It is run by Grelod the Kind with the help of Constance Michel. There is a cooking pot in the fireplace in the main hall.
With the addition of the Hearthfire DLC, a new manager runs the orphanage and children are now available for adoption after answering several brief questions. They are sent to the homestead of the Dragonborn's choice (should more than one have been built).