In The Lord of the Rings film trilogy, Saruman lives in the fortress tower of Orthanc.
Orthanc stands at the center of Isengard, a fortified ring of walls in the southern part of the Misty Mountains region. Saruman uses the tower as both a residence and a base for studying the power of Sauron. Its black, sharply rising design makes it one of the trilogy’s most distinctive structures.
In The Two Towers, Saruman looks out from Orthanc while his Uruk-hai army prepares to attack Rohan. After the Ents destroy Isengard’s defenses and flood the area, Saruman becomes trapped in the tower. Gandalf later confronts him there, and the Palantír of Orthanc becomes an important object in the wider conflict.
Orthanc is not the same as Barad-dûr, Sauron’s fortress in Mordor. Nor is it Minas Tirith or Minas Morgul, both of which are Gondorian or formerly Gondorian strongholds.