The Spiritual tour includes the mosque bulit by Muhammad Ali Pasha.
We visited three mosques in Cairo. (1) The Mohammed Ali Mosque (also known as the Alabaster Mosque), is very close to the Citadel. It's a very nice mosque, especially if you haven't seen a lot of mosques. (2) The Sultan Hassan Mosque and Madrassa is very old (14th century). (3) The Al-Rifa'i Mosque, also known as the Ali Pasha Mosque, is almost across the street from the Sultan Hassan Mosque. It's quite beautiful. I was surprised to find out that the Shah of Iran is buried at the Al-Rifa-i Mosque.
It's likely that you will visit all three on your tour. They aren't very far from one another.
Does the tour include the Coptic quarter?
The spiritual tour might make more sense on a first visit to Cairo (even though I would personally pick Saqqara).
Here is the schedule for Cairo:
Grand Egyptian Museum
I am guessing that your are talking about the museum in downtown Cairo. The Grand Egyptian Museum (GEM) in Giza is now scheduled to open in late 2024. Officials have been saying the opening of the GEM is six months out ever since I started planning my first trip in 2019, probably before. I will believe it when I see it.
However, I love the downtown museum. You feel like you are stepping back into the 19th century when you visit, and I have never experienced a museum quite like it. The wood and glass cases, the hand typed signage and the open windows makes you feel like you are stepping back in time. When I visited in 2020, they were just beginning to move some of the antiquities to the GEM, and when I visited again in 2021 they had moved considerably more to the GEM. As far as I know, though, the Tutankhamen death mask and many related pieces are still at the downtown museum. It is definitely worth the visit.
Giza Pyramids
Essential. You have to see them. Full stop.
Historic Cairo-Moez Street, Khan el Khalili
It's interesting. Definitely worth doing.
Free day or one of the two tours in my original post
They are also offering to arrive one day early for a visit to the
Royal Mummies Museum.
Depends on how much you like mummies. I saw the mummies while they were still at the downtown museum, and I saw them again at the their new home. The nice thing about the the new mummy museum is that they have a broad overview of Egyptian history from pre-historic times to the near-present. The other museums all concentrate on the pharonic periods.
What is your opinion on that? Two full days in a row at museums: the
Royal Mummies Museum followed by Grand Egyptian Museum.
If I had to pick, I would choose the old downtown museum over the mummy museum. However, there is not much overlap between the two, and so you won't be duplicating much by visiting both.