Surely, Egypt and Jordan are very good destinations to go and there are many interesting sites to see and visit.
Here are the best sites:
Pyramids of Giza are the top attractions allover Egypt and there are many travelers visit this amazing site every year.
Luxor and Aswan, those two cities hold almost one third of the ancient monuments of Egypt and the best way to visit is by Nile cruise or Dahabiya.
Petra is the second ancient attraction after the great Pyramids of Giza and it is worth visiting.
Dead Sea is considered to be the lowest point on Earth and very interesting place to visit.