Egypt Trip Planning
 

I am traveling solo to Egypt in April.
Arrive on April 13th at midnight in Cairo and Leave on April 21st at 9pm from Cairo.
This is what I am planning on:
April 14th - Cairo - see the city
15th: Cairo - Pyramids
16th - Aswan (fly to Aswan early morning.)
17th - Aswan
18th - Aswan
19th - Luxor
20th - Luxor
21st - Fly from Luxor to Cairo around Noon so that I can make the evening flight back to the States.

I would like to take a day or 2 day nile cruise - is that possible?
Is Red Sea too far or is it doable?
I like culture and architecture.
Any suggestions?