Is it permissible for me to travel with one of my female friends to visit family?

A woman is not permitted to travel or be in seclusion except with a mahram, due to the Prophet's (peace be upon him) saying: "No man should be in seclusion with a woman unless she has a mahram with her, and a woman should not travel except with a mahram." Therefore, your travel together is not permissible if you are a stranger to her, and it is not permissible in Islam to establish a relationship called a "girlfriend" or "mistress."