Although that's true, and Gandalf's Sindarin name
Mithrandir even means 'Grey Wanderer' or 'Grey Pilgrim', he did have a permanent home: Valinor. He just didn't go there for most of the Third Age.
During his time in the Hither Lands he lived everywhere and nowhere, dividing his time between the various places to which his mission took him. He even says of Tom Bombadil in LotR: "He has been a moss gatherer ; and I have been a stone doomed to rolling".
In HoME XVI, the Valinórean land of Dun Rómin is named as the place of Olórin's retirement after his return from the War of the Ring. *
* Not really
