In Assassin's Creed, the Assassin bureau headquarters where Altaïr begins is in Masyaf.
Masyaf is a fortified mountain settlement in modern-day Syria and serves as the main base of the Levantine Assassin Brotherhood. Altaïr Ibn-La'Ahad returns there after an unsuccessful mission at the start of the game and is demoted by his mentor, Al Mualim. His subsequent missions begin and end at Masyaf.
The fortress is based on the real medieval castle of Masyaf, which was associated with the Nizari Ismaili community. Assassin's Creed uses that historical setting while presenting a fictionalized conflict between Assassins and Templars.
Acre, Damascus, and Jerusalem are important target cities that Altaïr visits, but none is his headquarters. Their inclusion in the game's memory sequences can make them seem equally central, while Masyaf functions as the Brotherhood's home base.