One of the most worthwhile things to see and do in Cairo is visit Dahshur, a royal necropolis in the desert, where the oldest true pyramid, the Red Pyramid, can be found. Some of the burial sites and pyramids date back to the Old Kingdom of the 4th dynasty and the Red Pyramid and the Bent Pyramid were built by Sneferu in about 2600 BC. The Bent Pyramid is so-called because the angle of it's sides is not quite straight, probably the result of an ancient engineering mistake. The Red Pyramid, made out of red limestone, was built after the Bent Pyramid and is thought to have been the first true, straight-sided pyramid in Egypt. The famous Pyramids of Giza were modelled on this design. You can climb into the Red Pyramid and descend down a tunneled ramp into its three interior chambers which is a rare privilege. There are other tombs of interest scattered around the area and you can't walk far without stumbling on some wondrous ancient ruin.
Dahshur is about 20 miles (32km) from Cairo and makes for a fascinating excursion from the city. The drive takes under an hour and follows a scenic route which passes through date orchards. Dahshur is far less crowded than most other big tourist attractions and visitors experience none of the hassle from locals and touts that they do at Giza. At this site you can still get the thrill of an explorer discovering something mysterious and ancient.
However, the empty nature of this famous archaeological site is partly due to recent sectarian violence in the nearby town of Dahshur (July 2012), so travellers are advised to be alert.