The pyramids and Sphinx early in the morning, lunch nearby, then the Grand Egyptian Museum in the afternoon. Stay for a late Wednesday or Saturday opening.
Day 2
Islamic Cairo
Al-Azhar Mosque, Al-Muizz Street and Bayt al-Suhaymi, then Khan el-Khalili and dinner as the lamps come on.
Day 3
Citadel & Mamluk Cairo
Sultan Hassan and Al-Rifai in the morning, the Citadel at midday, Ibn Tulun and the Gayer-Anderson Museum after lunch, sunset at Al-Azhar Park.
Day 4
Old Cairo & the Nile
The Hanging Church and the Mosque of Amr ibn al-As, the National Museum of Egyptian Civilization, then a felucca at dusk.
Day 5
Saqqara & Dahshur
The Step Pyramid, the painted tombs of Saqqara and the Bent and Red Pyramids, with far fewer crowds than Giza.
Day 6+
Go deeper
Alexandria by train, the Fayoum oasis, or a slow day of Zamalek cafés, the Egyptian Museum in Tahrir and Downtown’s old façades.
Honest thought: Cairo traffic is heavy and distances are long. Plan one area per day, start early, and leave Giza and the old city for separate days. Late afternoon is the worst time to cross the city.