The Wild Nature of both Petra and Wadi Rum and the unbelievable city of Petra, combined, will definitely amount to a 2 night-3 day tour to South Jordan. 
Visiting The important Crusader Fortress of Shubak and Jeeping + Hiking to Aaron's Tomb will enrich your experience greatly.
Getting to South Jordan involves a flight from either Tel Aviv or Ben Gurion Airport to Eilat and crossing into Jordan or, alternatively, being driven down south by your tour guide, seeing places on the way, and than crossing. the latter option will result in a 3-night stay in Jordan. every option involves an identical way of return - either flight or Tourist van.
You could choose between a 5-star hotel, a 3-star hotel and an authentic Beduin Tent & Food. sleeping in the tent is both fun and authentic and could involve an early morning balloon flight as well as a later Jeep Tour.
A visit to Petra is, needless to say, a MUST! it is one of the most amazing Archaeological sites you would ever see in your life.
in anycase, this is the kind of tour that will leave you stunned!

Jordan is no less than heaven for fans of History, Archaeology and adventure.
You will be surprised at how much more this country has to offer than just Petra!
Petra is obviously in any trip to Jordan, but Jerash is one of the best-preserved Roman cities in the world and Madaba has an exceptional mosaic floor as a 1500 year-old map. The nearby Mount Nebo is where Moses saw the Promised Land yet couldnt enter it, and Amman is a vibrant Arab Metropolis with plenty of Oriental charm, mosques, Markets, interesting Museums and Biblical sites. The Kings' highway and the Awe-inspiring Wadi Al Mujib will bring you to Kerak, an all-mighty Crusader fortress, and the nearby Dead Sea provides Excellent & inexpensive accommodation options as well as the Baptismal site of Jesus by John in Bethany on the Jordan River.
it is a combination of Ancient & Current History, beautiful views, unique nature, Biblical Scenery and sites, all in a country of stability. All tourists, never mind their background, find that whether you travel on a budget or on a 5-star level, Jordan is easy, interesting and fun. 
The Warmth and kindness of its people is everywhere, so visiting more of Jordan will definitely assure you a better trip!
It is the kind of country where tourists ask themselves, once there, "how come we havent planned to spend here more time?!"
You have the chance to plan beforehand to be there enough time - just do it!
 

Israel's neighbor from the East is a wonderful, peaceful and stable, filled with pleasant people as well as World-Class hotels.
Jordan is the Land of the Bible as part of Western Heritage as much as Israel. it is a country sprawling with Historical and Archaeological Sites, which will definitely leave a mark on you, irrespective of your background.
You could choose between a 5-star and a 3-star option, but in anycase a trip to Jordan is Fun, Safe and interesting.
Any trip to Jordan involves Seeing Petra, but assuming you dont know when you will be back (if at all...), in a matter of one week you could pretty much see almost the whole country.
If Nature, History, Bible and Archaeology are you thing, This kind of a trip to Jordan is perfect!
You could fly from Israel to Jordan for 30 minutes, or cross with a VIP service at the Sheik Hussein border crossing, next to Bet Shean. 
We would start in Northern Jordan with a visit to Umm al-Qeis, otherwise known as Gadara, in the Land of the Gadareens from the New Testament, and view the Sea of Galilee from afar. than we would continue to one of the Dessert Fortresses, beautifully decorated with Frescos from Early Islam.
In Amman, the Capital City, we would visit the Biblical Site, the markets and spend our first night.
The next day we would embark to Ajlun for a visit to the gorgeous Muslim Fortress, followed by a visit to one of the best-preserved Roman City in the world, Jerash, definitely one of the pearls of the whole trip.
In The afternoon we would be back in Amman, with a visit to the original Philadelphia and its Theater. a visit to the Archaeological Museum would reveal what's the story behind Indiana Jones!
After spending another night in Amman, we would visit on our Third Day the Outstanding Car Museum, and continue down South to Hisban, where the Bible will come alive when we read from it. further down south is Madaba, with its unique Mosaic Floor Map from The 6th Century AD. After Lunch we would continue to Mount Nebo, and get to see what Moses saw more than 3000 years ago (only he didnt get to visit it, like you...).
Than you could choose between 1-night stay in either one of the hotels by the Dead Sea, in Madaba itself or in a Spa Hotel next to a wonderful 150-foot tall Hot springs. whatever you choose will be relaxing for you!
On your fourth day we would Visit Mukawer, the place where John the Baptist was executed, also known as "Massada of Jordan". than we would continue to Umm-al-Rasas, a world heritage site known for its amazingly-preserved Mosaics.
After lunch in Kerak, we would visit the formiddable Crusader Fortress, and than drive Along the Kings' Highway and Wadi Al Mujib to Wadi Musa, where we would spend our 4th night.
We would start the 5th day with a visit to the Carved-out-of-the-bed-rock Nabatean City of Petra, one of the 7 wonders of the world. after lunch an optional tour will involve Jeeping and some Hiking to the Awe inspiring Views from the place of Aaron's Tomb.
After another night in Petra, we would relax in the morning of the 6th day, enjoy the Hotel Facilities, and leave in Early Afternoon to Wadi Rum, the Battle Scene of Lawrence of Arabia during WW1, enjoying a Sunset Jeep Tour and an Authentic (Authentic!!) Beduin Dinner, spending a night in a Beduin tent.
On our last day, we would start at the crack of dawn with a Baloon Flight above Wadi Rum. after breakfast we would catch on some sleep while driving along the Arava Valley, stopping on the Way in Jesus' Baptismal site on the Jordan River, and make it back in late afternoon into Israel - Happily and everafter!