This is probably the No. 1 three Day adventure ACTION PACKED tour in Israel!!
Day 1 from, Tel-Aviv to Eilat through the remarkably diverse Negev desert. Including multiple 4x4 rollercoaster like tracks, Geopolitical sites, world unique crater geology formations and Jewish Biblical anchors 3800 years old!
Day 2 at Eilat. One of THE MOST FASCINATING desert-coast-corals tourist attractions city in the world! This is a "free" day but the options are overwhelming, including day trip to Petra and Wadi Ram in Jordan, The amazing Hay-Bar Biblical Wildlife restoration project, King Solomon's Timna ancient coper mines park and the most famous coral reef sea-life snorkeling.
Day 3 is a focused 4x4 track of the Eilat Massif mountains awesome phenomena! I call it "The Creators geological playground".It is the pinpoint of two tectonic plates and the Arabian shield.  The interwoven geometries, colors and rocky mountains core, combinations, are COUNTLESS !!

Day 1

Ten hours from Tel Aviv to Mitzpe-Ramon, through some of the most amazing historic, geological and desert off road 4x4 scenery in Israel... 
The Ad-Halom Ottoman bridge and how close Israel was to losing the whole Negev desert in 1948;
The Sderot tree and understanding a deeper look into the Gaza Israel conflict;
Tel Harur, Grar land and Be'er Sheva. The first anchor established by Abraham in the land of Israel;
A focused off road 4x4 jeep track in Makhtesh Mitzpe Ramon east, the geological desert wonders and the Nabati spice route;
Deep in the Wilde southern Negev desert: Telem Tsichor and Bikat Tschicha.
Drive down to Eilat. Independent board & lodging.

Day 2 

Three options:
1- Free day on sunny beach and sports attractions. Eilat is a desert beach tourist city, so mountain biking, camel riding, scuba diving, wind surfing are all very common.;

2- Independent booking Rent a car and drive up to the famous wild life park Hay-Bar Yotveta. Time permitting, visit the Timna Park too.

3- An organized tight schedule tour to Petra and Wadi Ram. Petra was the Nabatian capital city over 1500 years ago and famous for its sand rock carved structures in the desert of Jordan.
Independent booking, price is 199$ for tour + 125$ visa & border fees into Jordan. Regretfully, I have no operator to recommend. Furthermore, I caution you to read all small print and TripAdvisor reviews of that operator.
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Day 3

This tour acquaints us with the most impressive, beautiful and off road 4x4 track through the Eilat massif nature reserve. We will track through Nachal Shlomo, walk up Ma'ale Gishron, climb Har Yoash, view Ein Netafim, walk the Red Canyon of Nachal Shani and cross moon like landscape of Meishar Seipim. 

Something in the atmosphere of the interwoven Eilat red, black and white desert mountains, may award you the feeling you are in a grand court of nature...All you need to do, is listen to the great power of creation and peace around you...
The "Eilat massif" landscape as it is called, is the only geological aria in Israel that revels core earth rocks originating from hot magma. Most of the rocks in Israel, were formed when this aria was under water, and millions of years of sea sediments produced white lime stone layers, later pushed up producing hills and mountains all over Israel and are known as "The Jerusalem Stone". The Eilat dark mountains are the true crust of our planet and are visible to us, owing to the desert conditions at Eilat, prohibiting vegetation coverage.
However! This is only half the wonder! How can the jagged red and black granite mountains co-exist with the "soft" and rounded lime stone mountains?... Driving through and climbing these mountains is definitely a wonder and an "on hands" geology class...