I did a nine day tour of Israel with Gate 1 (usually have awesome deals) and added my own stuff before and after. I went in March last year.
We nonrevved to Tel Aviv on EL AL from JFK and came back to PHX via Air Canada through Toronto. We planned to come back on Delta but a flight cancelled—we literally changed our listing using staff traveler and myidtravel while in line.
We stayed in Tel Aviv, Jerusalem, and up on Galilee. We went to Bethlehem, Masada, Dead Sea, Jericho, up north, etc. All over. The tour was awesome and cheap, like $1100 per person. They do all the driving and tour guiding plus provide hotels—you might consider looking into that.
After our tour we rented a car in Jerusalem and drive south to Eilat where we crossed the border into Jordan (on foot) and picked up a three day tour of Petra and Wadi Rum.
The driving in Jerusalem is hard core aggressive. Just drive like they do, and hopefully you can drive a manual.
Israel has awesome food. Jordan, not so much.
There is so much to see—look up a Gate 1 travel itinerary and you can get an idea what to see.