Anbar is Basim's home before he travels to the Hidden Ones' bureau in Assassin's Creed Mirage.
Mirage begins with Basim living in Anbar, a settlement near Baghdad, where he works as a street thief. His recurring nightmares and desire to escape lead him into contact with the Hidden Ones, the organization that serves as the historical predecessor of the later Assassin Brotherhood.
After leaving Anbar, Basim reaches the Hidden Ones' bureau in Baghdad and begins formal training under Roshan. The game then focuses on his development as an apprentice and operative during the Islamic Golden Age.
Baghdad is the principal city and setting of much of Mirage, which makes it an easy answer to confuse with Basim's original home. Anbar is the more specific location asked for here; it is not the same as the modern Iraqi city of Ramadi, although the names are historically connected to the region.