No, she travels between the underworld and earth yearly, which is the reason for the changing seasons in Greek and Roman myth.
Gods and Goddesses do not die.
Hades' wife is Persephone, Persephone is a Goddess. Gods and Goddesses don't die, they are immortal.
Persephone never died. She's a goddess. Gods and Goddesses can't die. They're immortal.
Persephone did not have a favorite: as all people die whatever their city.
Persephone does not have a personal city: the people of all cites die and come to the Underworld where she is Queen.
All people who die go to the Underworld, so Persephone need not have a favorite city.
All people die no matter the city, so no Persephone was not a patron goddess of any place or city.
Die, this was winter.
No: but all who die - in war or otherwise - come to dwell in the Underworld, where Queen Persephone and King Hades rule.
Hades and Persephone are King and Queen of the Underworld, that being the dwelling place of the dead: they, however, were both firmly immortals.
Every year, Persephone spends the autumn/winter (when plants die) with Hades, and returns with spring/summer.
All people die no matter the city, so no Persephone was not a patron goddess of any place or city.