In Assassin's Creed Mirage, Anbar is Basim's home before he joins the Hidden Ones.
Basim Ibn Ishaq begins the game as a young street thief living in Anbar, a settlement near Baghdad. After a dangerous encounter involving a mysterious artifact, he flees and eventually reaches the Hidden Ones' stronghold at Alamut, where Roshan trains him as an initiate.
Most of Mirage takes place later in ninth-century Baghdad, during the Abbasid period. The contrast between Anbar and Baghdad establishes Basim's movement from an uncertain life on the margins to a structured role within the Hidden Ones. His memories and visions also connect the story to wider Assassin's Creed mythology.
Baghdad is the game's principal urban setting, so it is an easy alternative answer. Masyaf belongs to the Levantine Assassin tradition in other games, while Samarra is another historic city of the Abbasid world. Neither is Basim's childhood home as identified in Mirage.