Can women go on a group excursion outside the city, and does the ruling on driving for this differ between women and men?

There is no harm for women to go out collectively for recreation, provided certain conditions are met: that the places are free from forbidden acts (munkarat), that they adhere to the legal hijab, that their departure is with the permission of the husband or guardian, and that the distance traveled does not constitute a journey (safar). A woman driving a car is permissible if it does not lead to any transgression of Islamic law. It is not permissible for a man to be alone with a woman in a car, but it is permissible for a group of women to ride with him in the car, provided there is no fear of temptation (fitna) and the distance is not a journey. It must be noted that the default principle is for a woman to remain in her home.