Tiber Island
Tiber Island is an island located on the river Tiber, in central Rome. During the early 16th Century, the island served as the headquarters of the Order of Assassins in Rome and as a base of operations for Ezio Auditore da Firenze's war against the Borgia. While Ezio went out undermining the Borgia's rule over Rome, Niccolò Machiavelli stayed on the island, training new Assassin recruits sent by Ezio. On the In-game map Tiber Island is marked by a white Assassin symbol on a black background.
Externally it's an unassuming building without anything that'd give clue to its purpose. Function wise it's similar with the Auditore villa in Assassin's Creed 2 and more: there's the armory and armor room to display the armor sets and weapons, gallary showcase the portraits of fallen targets, a hall that serves for ceremonial purpose (such as inducting new assassins into the order), a viewpoint at the roof that doubled as Leap of Faith platform for new assassins.
As Ezio recruit more apprentices into the Order, you'd see them milling about throughout the headquarters.