This 3-day Cairo, Egypt itinerary keeps each day on one bank, so the river is crossed once, in the direction the day is already going.
Day 1: Giza, the Pyramids and the Sphinx
Giza sits just west of the city, close enough that the plateau feels like the edge of Cairo rather than a separate trip. The Great Pyramid there is the last surviving Wonder of the Ancient World. It's also a must-do in Cairo; the Sphinx keeps it company, and a morning is what the pair asks for.

Walking the plateau
Start at the Great Pyramid and work down toward the Sphinx, since that is the way the ground runs and turning back at the top buys you a climb in full sun. There is no shade up there worth counting on, so a hat, water and a scarf matter more than a camera strap. From May to September, be at the site for sunrise, because the heat builds fast enough that a late start changes the whole morning.
Saqqara and Memphis, on a longer trip
Saqqara and Memphis sit south of Giza as a half-day run of their own, and Dahshur adds the Bent Pyramid and the Red Pyramid for a second desert stop. None of that fits beside a Giza morning, so it goes on a fourth day rather than this one.
Day 2: The Egyptian Museum, Tahrir and the Nile
Day 2 stays on the east bank and indoors through the hottest hours. That is not a compromise: the museum is the one stop on the trip where the temperature outside stops mattering.
The Egyptian Museum on Tahrir Square
The Egyptian Museum holds a collection that runs well past one morning of attention, and the Grand Egyptian Museum is adding exhibits of its own. Choose one of the two for your morning instead of splitting the day between them.

Tahrir Square and the Corniche
The museum door opens onto Tahrir Square, and the Corniche follows the Nile below downtown. Late afternoon is when that walk pays off: the river runs under the bridges, and the gardens on the far bank are the quiet side of the same view.
A felucca or a Nile dinner cruise
The evening has two versions, and you need one or the other. A felucca at sunset is the lighter version and leaves you on the Corniche in time for dinner. A Nile dinner cruise is the arranged one, meal and river in the same booking, and the single evening on this itinerary worth sorting before you fly.
Day 3: Islamic Cairo, Khan el-Khalili and Al-Azhar Park
The third day is the one people underestimate. Islamic Cairo is a working district rather than a single sight, and the bazaar at its middle is the busiest ground you will walk all trip.
Morning: mosques and the old streets
The lanes open into courtyards and Ottoman-era mosques, with a tea house every few doors. Dress for the district as much as for the heat: shoulders and knees covered, and a scarf that works at a doorway as well as in the sun. Modest dress is what people here expect, and loose cotton is cooler than a t-shirt anyway.
Afternoon: Al-Azhar Park
Al-Azhar Park is the green escape in the middle of it, with grass, trees, and city views, and the one place on day three where sitting still is the point. Take the hottest stretch of the afternoon there and walk into the bazaar with something left in your legs.
Evening: Khan el-Khalili
Khan el-Khalili belongs to the evening, when the spice-scented alleys fill up, the tea houses take on customers, and the quarter keeps going into the night.
End the night there rather than back at the hotel: the bazaar and downtown sit on the same bank, so the ride home is the shortest of the three days.
