In the original Assassin’s Creed game, Altaïr Ibn-La'Ahad is primarily based in Masyaf.
Masyaf is a mountain settlement in modern-day Syria and serves as the headquarters of the Assassin Order during the game’s 1191 storyline. Altaïr returns there between missions to report to Al Mualim, the order’s mentor, receive guidance, and advance the plot.
The game also takes Altaïr to the major cities of Acre, Damascus, and Jerusalem. Those cities are the main locations for investigations and assassinations, which can make them seem like the central base. Masyaf is different: it is the Assassin stronghold and the place most closely associated with Altaïr’s order. The game’s modern-day scenes take place in a laboratory where Desmond Miles experiences Altaïr’s memories through the Animus.