Alexandria has its streetcars. Cairo has a wonderful 'Metro' which is safe, clean and very cheap. It's a wonderful experience just mingling exclusively with the local women. Many will come up and talk to you, while laughing shyly. Very few tourists use these systems and, personally, I felt that the locals were impressed to see a foreigner on their transit system.
F lying from one destination to another in Egypt is safe, quick, cheap and reliable.
Train stations are bustling with thousands of people, so do take the precaution not to leave your luggage unattended and watch your purse or daypack. Get a porter to take you to the right platform. He will even position you at approximately the area where your car will stop. I t's nice to go out in the evening. While in Cairo, take advantage of attending local concerts or the opera.