Have been to Cairo twice, it is most definitely NOT safe to wander around unsupervised or without an Egyptian guide. Women should dress modestly, no cleavage shown, tight trousers, bare arms etc.
Sadly Egypt is getting more militant towards westerners, and although Egypt relies heavily on tourism, they are really not enamoured of westerners. Do not display handbags, cameras, walkmans, money belts etc.
Try to always go out as a group, if you want to see inside a Mosque, ask first just dont walk in as I did, then got pelted with stones !! The Pyramids are a must see and also the Egyptian Museum, but use caution at all times.