The capital was Memphis, then Thebes, then Cairo in the 900s. That means you have to venture out of the city if you want pyramids and royal tombs. However, The Pyramids of Giza aren't far outside the city and the Egyptian Antiquities Museum has done a good job of relocating high demand artifacts to the city.

Nav:

Pyramids of Giza: Iconic Egypt and only a 30 minute drive south of the city. Most tour operators offer transportation from your hotel. The pyramids were built for Khufu, Khafre, and Menkaure. There are several smaller pyramids built on the site that don't get any attention but they were built for queens of Egypt.
Pro Tip #1: Many independent operators offer camel rides in front of the Pyramids. I chose not to participate due to concerns for ethical treatment of the animals. I'm not a card carrying PETA member but the camels are often abused to make them compliant.
Pro Tip #2: If someone offers to take your photo in fun poses with the pyramids, they expect a tip and may press aggressively. Decide if and what you want to pay upfront.

Such big stones!
You drive by the Sphynx when exiting.
This is the free view on the way out.
If you pay extra to see the Sphynx up close, that's the area you get to go.

Egyptian Antiquities Museum: Key highlights include the mask of King Tut (no photos allowed). A tour guide is a must if you want to make sense of what you're seeing here. Guides are available outside (conveniently located near the ticket booth).
Pro Tip: Guides charge by the hour so research current rates before your trip. They also expect a tip and will press you for one as a cultural insult if you don't provide one. Also, they will try to start the time from the time stamp on the ticket. Negotiate this up front as to when the tour starts. Remember, you decide when the tour ends and where the guide should take you. My tour was about two hours.

Ornate canopic jars for holding organs removed in the embalming process.
Canopic jars in an alabaster covered sarcophogus.
A scribe (record keeper)...so valuable to the Egyptian people, they put his face on the 200 Egyptian Pound note.
Not everyday you see a mummified baby with gold leaf.
King Tut's chair.
Gold was rare enough to be valuable to elites...
...but silver was expensive and showed real wealth.

Coptic Cairo: The Christian stronghold in the city before Islam arrived in the 600s. I'm glad it's still around. There are several orthodox churches to see and a graveyard (with limited access). You can easily get a guided tour with pickup from your hotel. I used the subway and found an audio tour. You can't take photos of the graveyard.

Babylon Fortress...built around 30AD by the Romans.
St. Mary's Church
St. Mary's interior
'The Hanging Church' because it's partially built over an underpass.
Church of St. George...original was destroyed so this one is a bit over 100 years old.
St. George's interior
Gardens and paved walkway to the graveyard and some churches.

The Cavern Church St. Sergious and Bacchus...tradition holds this is where Joseph and Mary brought young Jesus to escape the wrath of King Herod.
St. Sergious and Bacchus interior
The subway. It uses tickets you can buy at the counter.

Saqqarah: This is the new hotness on dig sites. At least from watching the Netflix shows with Zahi Hawass and others in the archeology field. You can find some royal tombs here but also burial sites of the noble class. You won't find artifacts here but architecture and archeology.

The front is the fanciest part.
Just beyond the gates is a great place for a photo op...when no one else is around.
The step pyramid of Djoser...believed to be the first pyramid from which the others were crafted.
Temples surround the temple.
The relief detail is fantastic.
If these walls could talk...
...oh, they do...
...if you read hieroglyphics.

Nosh:

Taboula Lebanese Restaurant: Comfortable interior and some traditional Lebanese specialties.
Pro Tip: It's located in the area with the foreign embassies so expect road closures and route alterations that don't come up on GPS if you're walking or driving yourself.

Fattoush 'Tabloua'...veggie salad with fried pita.
Eggplant fatteh
Shish taouk motafae...chicken with mushrooms. The lemon sauce was very bitter.
No matter your party size, this place can handle it.

Nip:

Sakara Gold: It was the best of the local lagers I tried.