In the original Assassin's Creed, Masyaf serves as the Assassins' main headquarters in 1191.
Masyaf is a mountain settlement in present-day Syria and is portrayed as the home of the Assassin Brotherhood led by Al Mualim. The game begins there, establishing it as the central base before Altaïr Ibn-La'Ahad receives his missions.
The story then takes Altaïr to three major cities: Jerusalem, Acre, and Damascus. Those cities are mission locations, not the Brotherhood's headquarters. This distinction is a common source of confusion because much of the game's action happens away from Masyaf.
Historically, Masyaf was associated with the Nizari Ismaili state and its fortress. Assassin's Creed combines that historical setting with fictional characters, technology, and events to create its 1191 narrative.