Praise be to Allaah.
It is not permissible for a woman to travel without a mahram because of the general meaning of the hadeeth of the Prophet (peace and blessings of Allaah be upon him): “It is not permissible for any woman who believes in Allaah and the Last Day to travel except with a mahram.”
And because the purpose for the mahram being there is so that he can protect her and take care of her, especially if any emergency arises, and travel is subject to emergencies regardless of the length of time involved. Whatever people regard as “travelling” is like this, and is subject to the rulings on travelling.
For more on the rulings on mahrams, see Question # 5538
Sheikh Muhammed Salih Al-Munajjid