Word or phrase for someone claimed as one of a city's own
One such phrase, though masculine only as far as I know, is favorite son. AHD (2) has:
A famous man viewed proudly by his hometown for his achievements.
an honorary citizen.
honorary "An honorary title or membership of a group is given to someone without their needing to have the necessary qualifications, usually because of their public achievements."
"Isambard Brunel was an honorary citizen of Bristol"