First and mostly - "La, shukran" (No, thank you), rinse and repeat. Lots of people will try to hand you things and help you get from Point A to wherever. I had some rudimentary Arabic when I went, which went a long way, but that is the most important thing.
I was backpacking at the time, so I don't have much advice on nice stuff. Echo the others on Cairo - craziness, Pyramids, Egypt Museum, the main sites are definitely worth doing. I got lost trying to find the khan al-khalili one day and just wandered around, which was interesting but not necessarily recommended. I actually found the subway to be pretty nice getting a couple places.
Didn't boat trip down the Nile, but Luxor and Valley of the Kings were lifetime highlights. The temples and tombs in and around Luxor are beautifully preserved and made me feel like a fleeting blip in human history more than anything else I've done. It was also the hottest I've ever been, at over 120F in August.
As to Red Sea diving, I understand the towns have changed quite a bit, but 15 years ago, Hurghada was a dump full of rude Russian tourists, Sharm looked like a normal resort town but I just passed through it, and Dahab felt like a paradise after the heat and bustle of Cairo, Luxor and Hurghada. I stayed in a backpacker camp/hostel in Dahab, and found one of the better dive shops I have ever worked with in the town. I understand the hotel/resort options have really built up there, which was already in progress when I visited. I extended my stay there from 5 days to two weeks and got an advanced dive certification, but would have to dig out my logs to remember what all I did (other than the big ticket items like Blue Hole and the Bells). I also did a sunrise bus tour to Mt. Sinai and St. Catherine monastery while I was there.
Happy to weigh in on particular questions if you have them, though with dive stuff especially, 15 years is a lot of time. And overnight buses around the country are probably not how I would travel anymore, but I have thoughts on those as well.