Ok, I was in Cairo in 2007. With the tensions some may have changed, but here are my suggestions:
- Alexandria - it's only a few hours away, and there are connections to get there (my tour company just offered a day trip before the tour started). It was fantastic and I'm so glad I got to it - the new Great Library is cool, lots of old monuments and Egyptian heritage around, and the seafood was so good!
- the churches - there are a variety of historical churches. This is important because as Egypt is now 97% Muslim, it's important to realise that this wasn't always the case. There are three main ones I'd recommend - the Coptic Church, the 'Hanging Church' which is something to be seen to understand and is also allegedly where the Holy Family stayed at one point, and of course, the Citadel and Mosque of Mohamed Ali Pasha up above Cairo for a spectacular view, although quite smog filled.
- Obviously, the pyramids and Sphinx in Giza. Easy to get to, and yes, you've seen them a thousand times in pictures, but nothing beats seeing them in person. And it blew my mind that you were actually able to enter one - made my day! Not good if you're claustrophobic though.
- Egyptian Museum - I was shocked that I actually had to argue with my group to extend a 30 min visit to 45 minutes for this. Fortunately we had a rest day when we came back through Cairo, so I was able to spend most of a day here - it's spectacular, an absolute gem if you like your history, and even if you don't - the Mummy Room - with kings and queens of past - it's incredible that you can be so close to royalty in that way (if a little weird).
There are obviously lots of local attractions like the Nile felluca rides, sheesha, and the Cairo Tower, but I'm trying to write about trips that take a good part of a day, if not all of it. I hope that helps.