According to me the most sight-seeing spots of Egypt was Pyramids of Giza, Abu Simbel, Great Sphinx, Valley of the Kings and King Tutankhamen, Luxor, Felucca Boat Ride, Red Sea Coast, Khan-el-Khalili, Cairo, Mount Sinai. But as per my personal experience, it will better to contact with the best Egyptian tour company like Imperial Egypt. They will suggest you the best one.
Cairo to see the Great Pyramids and the Egyptian Museum. Luxor to see the Valley of the Kings and Karnak Temple. Aswan to see Philae Temple and Abu Simbel. You can take a Nile cruise up or down the river between Luxor and Aswan. Take some relaxation in Hurghada and enjoy the Red Sea.