Praise be to Allah.
The saheeh Sunnah indicates that it is not permissible for a woman to travel without a mahram. This includes both long and short journeys, according to the majority of scholars. Everything that is called travelling is forbidden to a woman unless she has a mahram with her.
Al-Bukhaari (1729) and Muslim (2391) narrated that Ibn ‘Abbaas (may Allaah be pleased with him) said: The Prophet (peace and blessings of Allaah be upon him) said: “No woman should travel except with a mahram, and no man should enter upon her unless there is a mahram present.” A man said: O Messenger of Allaah, I want to go out with such and such an army, and my wife wants to go for Hajj. He said: “Do Hajj with her.”
Al-Nawawi (may Allaah have mercy on him) said, explaining that travel here does not refer to a particular distance:
What is meant is that everything that is called travel is forbidden to a woman without a husband or mahram, whether it is three days or two days or one day or twelve miles or anything else, because of the report of Ibn ‘Abbaas (may Allaah be pleased with him), “No woman should travel except with a mahram.” This includes everything that is called travelling. And Allaah knows best. End quote.
Al-Nawawi, Sharh Muslim (9/103).
In Fataawa al-Lajnah al-Daa’imah (17/339) it says: It is haraam for a woman to travel without a mahram in all cases, whether the distance is short or long. End quote.
See also the answer to question no. 101520.
What counts here is what is customary among people. If people regard it as travelling, then it is travelling, and it is not permissible for a woman to set out on such a journey except with a mahram.
Going from al-Qalyoobiyah to Cairo is not customarily regarded as travelling, rather there are many areas in al-Qalyoobiyyah to which it is easier and closer to travel than between one part of Cairo and another.
Based on this, there is nothing wrong with going from al-Qalyoobiyyah to Cairo to attend to your needs without a mahram.
And Allaah knows best.