Neighboring Heliopolis, Nasr City is the largest district in Cairo, sitting between the airport and Old Cairo. It is densely populated. The best bet for running is Child Park, off which has lovely paths where you can do a 1-1.5 km loop.
For a longer run, head for 2 km over to the International Garden, via Makram Ebeid and Mostafa El-Nahaas. In the International Garden, there are about 1 km of paths.