I would think easiest option would be to fly down to Cairo, it's pretty cheap and quick, you can check
EGYPTAIR - Welcome to EGYPTAIR website
Hotels close to the Pyramids is another matter, I have use
TravelRepublic in the past and have found some reasonable hotels through them.
You will need to take a taxi from the airport, not sure about the fare but it will probably cost you 150-200 EGP (someone else might have a better idea on that)
I have a contact there, she is a good tour guide and can arrange transfers and show you Cairo, probably worth paying her for a day or so, I have used her to arrange a private car with driver for a day which worked out pretty good, and a lot less hassle.