I just rented a car and drove, for like 15 hours a day. It's... indescribable, to touch the stones where Napoleon walked and Roman troops marched, or to look at the place - where even the stones are burned white and lifeless by the sun - and where men fought to hold, or take, every single inch of that territory. The sense of wonder, if you have any interest in or involvement with history, is immense.
Go see the Masada, and catch Ein Gedi/Mitspe Shalem on the way (lowest spot of land in the world.) Dip your toes in the Dead Sea. Take a drive up and see the Rosh HaNikra grottoes, if you have the time; at least see the Baha'i Gardens, north of Haifa (you've never seen anything like it in your life, I promise.) Go see the apples (!) growing along the northern border, and Mount Hermon should be nice and cool about now. Go by Ma'ale Adumim, and watch the tiny Bedouin kids running like mad and chasing the goats they're herding... in heat that would kill you or me in a couple of seconds flat. Take in Akko, and visit the little Greek taverna there. Drive up to the mountains above Kinneret, and take the road down to the Sea of Galilee. The crater in Mitspe Ramon... the Tel Aviv beaches - my GOD, the girls!!! - oh, and catch the shuk (street market) by the beach in TA!
...hell, I'd better stop before I hyperventilate. It's a place I'm totally crazy about, and I could rave about it for days.
There's a million places to see. I'll be heading there this year, this time for a good long stretch. Enjoy your visit!