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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.