Fallingasleep has it down pretty good. I would stay at the Nile Hilton or Ramses Hilton since they are walking distance to the Museum.

Do NOT talk to anyone who comes up to you at the airport. They are there to con you into a lousy tour. They have all sorts of official ID's, but they are working for themselves. Have the Hilton provide transport to the hotel where the concierge can advise you better.