I was there last winter. Spent a few days in Cairo, but most of the time in Dahab by the Red Sea.
To be honest, it was basically three weeks of really crappy food, but with a few notable exceptions. In Dahab, almost all seaside restaurants have an identical menu, where the vegan choice is restricted to stir-fried veggies with rice. Your best bet at a vegan-friendly breakfast is to take the Egyptian one, where you get falafel, fool (mashed beans), hummus/tahina, pita bread and cheese (regardless of how many times you explain that you don't eat it). sometimes you get fried potatoes and fried aubergine with that as well. finally I just gave up and bought some pita bread and tahina at a shopping mall instead.
Actually, the only good meals I had when I was there were once when we were diving by the Blue Hole and I got a large plate of tahina and pita bread for breakfast and the other time was when we got lost in Islamic Cairo and found this small hole in the wall where they sold falafel to the neighborhood. That was possibly the best falafel I've ever had.
Another vegan dish that's quite common is kushary, which is pasta, rice, lentils, chickpeas, roasted onion, tomato sauce and a spicy sauce. It's like a national cuisine, so usually quite easy to come by. The downside is that the ingredients are often prepared in the morning and are left out all day, so you might want to avoid spending long stretches of time in the absence of toilets afterwards. Of course, that depends on how adventurous you are.. ;) (I never had any major problems with my stomach during the three weeks I was there, tho.)
Oh, if you're going to dive in the winter, make sure you bring lots and lots of warm clothes. Seriously. I had more clothes on me when I was in Egypt than when I left home in the end of December.
The pyramids are incredibly exploited and the British Museum is floor after floor with cabinets full of old stuff without labels. The diving was cool. (Check out Big Blue in Dahab, they are great.)