Quick Orientation :
Alexandria is a lovely Mediterranean sea side town 3 hours drive away from Cairo but has its own international airport too.
Port Said & Port Suez are along the Suez Canal. A lot of people who work in the shipping industry are posted in these towns.
Sharm el Sheikh & Hurghada are the party towns on the Red Sea Coast.
Luxor, Aswan are in Upper Egypt and are the ancient pharaonic towns.
These are the main cities that expats live in.
I'm not qualified to elaborate on all the cities. Cairo is the only city I have enough knowledge about to share information on places to stay. So here goes...
Where to live in Cairo :
Big rule of thumb : STAY AS CLOSE AS POSSIBLE TO AREA OF WORK OR STUDY !
Traffic in Cairo means that it can take ages to reach from point A to point B. It's better to live as close as possible to your office or college/university so you can save a ton of time on traveling and use that time more productively.
If you are an Expat with kids then your child's school is another major consideration to keep in mind. Which school ? How long will it take my child to travel from home to school ? Is there a school bus facility ? Is there a convenient pick-up location ?
In a toss up between your own/spouses office location & child's school location, you need to take a call for yourself and your family that will best suit your needs.
If you are a student, then you may also like to stay in walking distance to a Metro station. The Metro service in Cairo is efficient & extremely beneficial to anyone who doesn't have their own means of transportation in this city or who doesn't want to drive here. :)
Areas to live in :
There are bungalows (stand alone houses) 2/3 floored buildings as well as a couple of highrises around roads 200 & 201.
Rents are higher in this part of town. But its worth it for the benefits of the greenery and community living.
Zamalek : An Island on the Nile in the centre of the city. Its the location of choice for embassy employees (a lot of embassies are located in this area) and AUC students. The AUC hostels are also located in this area.
The constructions are older here but not necessarily in bad condition. The apartments are really huge and spacious with high ceilings and wooden floors.
Garden City : Similar to Zamalek. Rent rates would be slightly lower than Zamalek. Its just across the river towards Maadi.
Mohandaseen : The business part of town. Started as a residential area for engineers is the story I have heard. Its an extremely busy part of town.
Dokki : A residential area between Mohandaseen and downtown.
Most of the restaurants and clubs are clustered around these areas of town.
There are other areas of town that are cool to live in to. These include downtown Cairo, Heliopolis, Nasr City, 6th of October city and El Rehab City.
Excepting downtown (which is logically in the centre of the city) the others are on the outskirts of the city and it takes some time to reach the city centre from these locations. But they are better planned with more greenery, parking spaces and less traffic.
Nasr City is also home to City Stars the largest mall in Cairo. A shopaholics delight with tons of stores, restaurants, food courts and cinema halls. Read more at http://www.citystars.com.eg/
This is just a quick primer on some residential areas in Cairo. Rates will depend on size of apartment/house and location. For eg within Garden city itself similar apartments may rent for different rates based on quality of construction, amount the owner has spent on doing up the place etc.
So find yourself a good "semsar" - real estate agent - and happy hunting.
(I may write a post later on estate agents, so stay tuned)
Edited on 18 April 09 to add:
Egypt Today did a wonderful series on this topic a while ago, that I though could add to this post.
Suburban Joy: covers Cairo-Alex Desert Road, Sixth of October City, El Shorouk City, New Cairo and the Maadi Circular.
The magazine had articles on Shorouq, Kattameya, 6th of October City, Al-Solaimaneyah also. I can't find the links for them online though.