Saruman lives in the fortress of Isengard in The Lord of the Rings.
Isengard is a fortified circular area in the southern part of the Misty Mountains, near the Gap of Rohan. At its center stands the tower of Orthanc, where Saruman studies, makes plans, and receives visitors. The fortress was originally associated with the people of Gondor before Saruman took control of it.
Saruman’s occupation of Isengard marks his break with the White Council and the other opponents of Sauron. He uses the surrounding land for industry and creates an army of Orcs, including the Uruk-hai. The devastation around the fortress contrasts with the natural world that later overwhelms it.
Isengard is not the same place as Sauron’s Barad-dûr, which stands in Mordor. Minas Tirith is Gondor’s capital, while Dol Guldur is a fortress in southern Mirkwood associated with Sauron’s earlier activities.