The tower where Saruman lives in J.R.R. Tolkien’s The Lord of the Rings is Orthanc.
Orthanc stands within Isengard, a fortified ring of land at the southern end of the Misty Mountains. Saruman uses the tower as his stronghold while serving as the head of the White Council and later betraying the other Free Peoples. Its dark stone and great height make it one of the most recognizable buildings in the story.
The Ents attack Isengard during the War of the Ring. After the destruction of much of the surrounding fortress, Saruman is confined to Orthanc for a time, though he later escapes through negotiation and deception.
Barad-dûr is Sauron’s tower in Mordor. Minas Morgul and the tower of Cirith Ungol are also associated with Mordor, but neither is Saruman’s home. Orthanc specifically belongs to Isengard and Saruman.