Alexandria is a possible day-trip. Enjoy a day visiting the library, a museum, fortress or the beach and return to Cairo after a good fish meal and maybe a drink. A first-class train ticket will cost about 52LE and 35LE for second class each way and takes about two and a half hours timetable from Egyptian Rail is available here, (http://www.egyptrail.gov....).
Ain al-Sukhna is the closest Red Sea resort to Cairo and easily reached on a day trip. This place is growing rapidly to become the getaway for Cairo's moneyed elite. To get here, hire a taxi for the day for about 200-300 LE.
Fayyoum is another popular place for Egyptians to picnic. While the city offers little in itself, the Qaroon lake and Wadi Al-Rayyan both offer scenic spots for relaxing and the area also contains some of the first pyramids in history. Get there by bus and then get a taxi to drive you around for the day at approximately LE 100 or get a taxi from Cairo at LE 200-300. It's possible to stay overnight at the scenic Tunis village for 30 LE.
The pyramids of Saqqara, Memphis and possibly Dahshur all offer an easy day trip out of Cairo. Expect to pay at least LE 150-200 for a private taxi.
Helwan the Japanese Gardens in Helwan 20 mins drive from Downtown or by The Metro is a perfect place to spend an afternoon picnic away from the city.
6th October City has 2 large American Style Theme Parks and is a 30 minute drive from the Pyramids at Giza.
Desert safari to Bahariyya or Siwa is also possible.