A 7-letter word for the place at which someone lives is "resides" or "domicile." Another common 7-letter word for where someone lives is "housing." However, the best fitting common single word for a place where someone lives with exactly 7 letters is "domicile" or "resides" depending on context. "Domicile" is more noun-focused as the place itself, while "resides" functions as a verb meaning to live somewhere.