Hi @yourace . I have been to Egypt three times now, last visit I stayed three months. Lots of information I could give you as I also used to organise tours there for a friend of mine who is a tour guide there. But to answer your questions, it’s a little hard as both Cairo and Luxor are great, both with amazing historical sites. Egypt is one, big historical site!
As you only have a week, I cannot stress enough the importance of having a registered guide. Their expertise and tips are worth their weight in gold I promise you! Also, as you say you would like to immerse yourself in the local culture, you won’t find a better way to do that than to spend time with your driver and guide. I ended up staying with mine in his family home with wife and children! Cairo is overwhelming for a first time visitor and without a guide, you won’t get a full understanding of what you see and miss seeing some really great places. You will be completely overwhelmed and lose valuable time and money trying to do it yourself. I could write pages on places to visit so please do start researching a good, reputable and REGISTERED guide, they are very cheap!
Places like Saqqara, Memphis are outside of Cairo but shouldn’t be missed so you need a driver and guide. The pyramids of Giza, Coptic Cairo, Al-Azhar mosque, Khan el Khalili Bazaar, Monastery of St Simon the Tanner, Mokkatan mountain (little known place well worth a visit) , the Egyptian museum, the list goes on. You could do all these places in two or three full days but will be tired.
You “could” then fly to Luxor which really has some incredible historical sites. Valley of the King’s, Luxor Temple, Colossi of Memnon, Temple of Queen Hatshepsut, again you “could” do all these in two days very easily. But without a guide you will be overwhelmed and learn little, I guarantee you.
I have been to most places in all Egypt many times and still don’t do it without guides. If you did Luxor and not Cairo, you could do Luxor and Aswan together for a week, maybe do a Nile Cruise between both places, it isn’t expensive in western terms. But who goes to Egypt without going to the pyramids? And don’t just see them, spend hours walking around them, you will be surprised what you will find!
Anyway, Egypt needs more than I can write here. With a week you will be running,. Food isn’t really that good there, they eat a lot of lamb, kofta, and meat in general, red lentil soup and vegetables, but no food in particular is anything to write home about. Not that good. Street food is basically Koshary and Shawarma. Flatbread with falafel, eggs and beans for breakfast is staple.
So how about that! I could talk for hours, Egypt is like a second home for me but it isn’t for the faint hearted so please don’t even attempt to manage it by yourself. You will understand when you experience the traffic and the touts and the crowds. There are still donkeys and horses on the streets of Cairo, and Luxor, and animal welfare is pretty distressing so you need to be prepared. Animals are not treated well at all, generally. Not sure of your budget but be careful, it is definitely a city of touts and they will get from you whatever they can so you need to be on your game. Just buying a bottle of water they will try to double the price . Get that guide! I’m jealous and will probably be back again this year. Despite everything I’ve said, I absolutely love the country and the people but you absolutely need to be prepared for it. The population of Cairo alone is 22 million, population all Australia - 26 million. That’s how crowded the city is. Let us know how you get on.