In Assassin's Creed Origins, Bayek's hometown is Siwa.
Siwa is an oasis in Egypt's Western Desert and the home of Bayek, the game's protagonist. Bayek serves as a Medjay, a traditional Egyptian protector, and the opening chapters establish his relationship with the oasis, its people, and his family. Siwa also introduces the game's setting under Ptolemaic rule.
Origins follows Bayek and Aya as they investigate a conspiracy involving powerful figures in Egypt. Their journey takes them from remote desert settlements to major cities such as Alexandria and Memphis. The investigation eventually contributes to the formation of the Hidden Ones, the organization that precedes the later Assassin Brotherhood.
Alexandria is a major intellectual and political center in the game, but it is not Bayek's hometown. Cyrene is important to Aya's background, while Memphis is another major Egyptian setting. Siwa's geographical isolation helps explain why Bayek has a distinct local identity.