hang (up) (one's) hat
To live somewhere; to take up residence. I'm originally from the East Coast, but I hang my hat in San Francisco these days. I've been traveling around the world for so long that it feels strange to finally have a place to hang up my hat.
hang one's hat (up) (somewhere)
to take up residence somewhere. George loves Dallas. He's decided to buy a house and hang his hat up there. Bill moves from place to place and never hangs his hat up anywhere.
hang your hat
be resident. North American informal 2001 Kevin Sampson Outlaws End of the day though it ain't the Royal and that is where I want to hang my hat.