From the narrow streets between the churches in the Coptic quarters.
The only structure left from Babylon, a tower that belonged to the fortress built by the Romans in the 2nd century.
Old Cairo is really compact, and you can with ease cover a great collection of important Cairo sights in half a day. And even include a coffee and some shopping, too. The most attractive parts of Old Cairo are the Coptic quarters, with the Hanging Church, the friendly and attractive Coptic Museum, which reflects the period where ancient Egypt changed into Christian and Muslim Egypt. Around these two sights, lie a collection of churches which all seem to claim an important part of Christian history. Tucked away between them all is one of the few remaining synagogues still in use in Egypt. A short walk from this district will lead you to the first Muslim settlement of Egypt, the ruins of Fustat, and the first mosque in Africa, the Mosque of Amr.
BABYLON
But don't forget to check out Babylon, it is right between the Mari Girgis metro station and the Coptic Museum. Confused? It is of course not the Babylon of Mesopotamia, but its namesake. There are several theories to its name. One says that it were the Chaldean workmen from Mesopotamia who gave the now lost town its name. Another theory says that its name came from Bab il-On, meaning "Gate of Heliopolis". What remains now is only a Roman tower. It is in quite good condition, and was under partial reconstruction when I visited in 2003.