I was in Cairo on one day tour from Sharm, we didn't have much time to explore, I remember it as "running" trip. Egyptian Museum is really worth to see, Giza obviously and Old Town. Generally this town depressed me, it shocked me that people throw garbage behind windows so they have dumping ground as view from their apartments although I'm not expert as I saw the city from the coach. For pyramids one day is enough, for the city not, for sure it's interesting and worth to get to know.