Willie - may I offer another option? Take the bus from Cairo to the Sinai and stay there, either in Shar'm or in Nueba. The weather would be great, there are Jeep tours in the Sinai desert which is beautiful, the diving is world class in the Red Sea, and climbing St. Catarina is a great experience.
If you end up going straight to Israel, I would fly, as the total bus travel time is about 10 - 12 hours, depending on how long you wait for the bus at Taba. I think flights are limited as Arkia doesn't cover that route, although they may do the Shar'm route, in which ase you could combine the best of both worlds.
For only a few days in Israel, Jerusalem is a must, but keep your eyes open in the Old City. You might even consider a guide there to get the most out of your time.
Enjoy, and let me know if you have any specific questions.
Eli