In the first Assassin's Creed game, Altaïr Ibn-La'Ahad's main base is Masyaf.
Masyaf is a mountain settlement in modern-day Syria and the headquarters of the Assassin Brotherhood during the game's 1191 storyline. Altaïr returns there to report to his mentor, Al Mualim, receive new targets, and obtain equipment before traveling to other cities.
The game also features Acre, Damascus, and Jerusalem as major investigation locations. Those cities are destinations for missions, not Altaïr's permanent headquarters. This distinction can be easy to miss because the player spends substantial time in all four locations.
Masyaf is based on a real Syrian settlement associated with the medieval Nizari Ismaili community. Assassin's Creed combines that historical setting with fictional characters, reconstructed architecture, and its science-fiction framing device involving genetic memories.