Here are some ideas:
Maadi - Good if you want to live in Little America. A large percentage of the expat population lives in Maadi. If you have children this may be a good choice as the better American type schools are in this area. $$$$$
Zamalek - A great place for the 30-something single set and others that appreciate what he 30-something single set like. It is clean, green and the cultural center of Cairo as well as well located in the center of Cairo proper. $$$$$
Mohandiseen - Very close to Zamalek for 1/2 the price. $$$
Dokki - Next to Mohandiseen and Zamalek. $$$
Heliopolis - Very much like Mohandiseen, but with wider streets and more green area. Close to the President so few water and electric outages compared to some other areas of town. Not as many foreigners living in Heliopolis as Zamalek or Maadi. $$$
Nasr City - Next to Heliopolis, but in a direction that makes transport more difficult and more expensive. A bit of a concrete jungle. $$

The $$$ signs are just to give you an idea of which area will have more expensive flats than the others. Don't take that as gospel though. There are flats of all price ranges in all areas... and if your company will pay for your flat, who cares?

Happy moving.