I've been to Egypt countless times and can assure you that you will be very disappointed with Cairo. Cairo makes Tijuana look like Beverly Hills
It's cool to see the pyramids but to leave beautiful Alexandria and take a five hour trip total just to see them is simply not worth it.
Alexandria is an amazing place with so many things to do and so many amazing fresh seafood restaurants!
Montazah palace and gardens
Alexandria National Museum
Fort of Qaet Bey
Down town area & cornich - awesome shopping!
kom el shokafa catacombs
My seasoned advice to you would be to stay and enjoy Alexandria! Plan a trip back to Egypt when you can spend some time in Cairo and perhaps take a nile cruise which is truly worthwhile!