If this is your first time trip to Egypt, you need to plan carefully. The best way to travel the country is taking the train or bus. Both of these are unreliable especially the train. It is best to do a slow pace trip rather than rushing to take pictures without appreciating the history in front of your eyes. For

3 days One can choose to visit either Cairo and Giza, or Luxor.

7 days Cairo and Giza and Luxor can be combined at a relatively fast pace. First day for Cairo, then next in Giza, back to Cairo and next day take the train to Luxor, stay 2 days in Luxor, and then back to Cairo, and finally another day checking out Cairo before departure.

10 days One can also add one of these: Hurghada, Alexandra, or Abu Simbel to the one week itinerary.

15 days Sharam El Sheikh and red sea can be added to the 10 days trip.