Cairo:
Egyptian Museum,The Citadel,the bazaar,the oldest 'university', Nile River dinner cruise, the Sphinx and the Great Pyramids at Giza
Memphis,Egypt
Saqqara,Egypt
Alexandria:
Pompey's Pillar,the location of the Great Library,the Mediterranean
Luxor:
Temple of Luxor,Karnak Temple,Valley of the Kings
While in the government run shops you may feel safer, you get better deals amongst the locals. HOWEVER, no guarantee on quality or safety there.
I highly recommend going to Alexandria. While you don't have to spend alot of time there, it's called the "jewel of the Egyptian Coast" for a reason. Especially, if you like seafood!
please include price if possible.
THANKS NELLY