The tenor of the above posts, IMHO, is overly positive. While there is very little street crime in Cairo, a woman can get into lot of trouble by dressing in what is a very conservative fashion by Western standards.
Based on my experience there if I were a woman going there, I would be sure to keep my arms and legs fully covered as well as my neck and chest area.
When I was last there I observed the morality police walking around in pairs with sticks smacking any couples along the Nile who dared to hold hands.