Here is a summary of costs and tips for budget travellers coming from Israel, in chronological order. The same prices will apply to all Israeli citizens as well as most tourists (except citizens of Arab countries who pay less for the Petra entry ticket):

  1. Cab ride from the Eilat central bus station to the Yitzhak Rabin border terminal that leads to Jordan - 30 Shekels (this is a recollection - it may have been 35 shekels, though); price was negotiated, not according to the meter.
  2. Departure tax for departing Israel via the Yitzhak Rabin terminal (Eilat) - 98.50 shekels. The departure tax is paid in cash. N.B. you pay the fee at one counter, and then you line up at another counter at which they look at your passport and where you get the actual exit stamp. If there are a lot of people at the border terminal and you're in a small group, one person may want to line up at the departure fee counter and pay for everyone  (they'll get a receipt showing that they paid) while the rest of the group stands in line at the passport presenting counter. That way you save time.
  3. After getting the exit stamp, visitors walk across to the Jordanian terminal (very short walk). Here you present your passport, wait about 15 minutes and then get your passport and visa. Very simple. There was no fee for entering Jordan.
  4. Taxi from border terminal to Wadi Musa/Petra: The taxis to Petra are right outside the terminal. There's a monopoly there so a traveller's bargaining power will be limited. If you have time and if it`s not Friday, you can take the bus (you`ll need to get to Aqaba first).It's about 52 Jordanian dinars (JD) for the cab ride to Wadi Musa. This is well above the expected price (35 JD), even after some hard bargaining (in Arabic). N.B. The taxi ride price is final. There is no tip that needs to be added when you arrive.The cab ride takes about 2-3 hours.
  5. At the Petra Gate Hostel, operated by Naser (Abu Rukan ?), a room and breakfast is 24 JD for one night with private bathroom, heating and hot water (if you shower at the right time of day). The hostel is basic but the owner makes a good impression. Make sure the sheets are clean on your arrival, or better yet, bring your own.
  6. Taxi rides within Wadi Musa to Petra. The Petra Gate hostel is about a 20 minute walk to the Petra site, or a 1-2 JD cab ride (5 minutes). It`s a bit of a longer walk getting back from Petra, because you have to go uphill. Taxis coming from the site back to the hostel will generally try to charge more (3 JD) and very few will agree to take visitors back for 1 JD (if you pay 2 JD you're doing ok).   
  7. Entry to Petra (The actual site) - 33 JD for a one day ticket, 38 JD for a two-day ticket. These are the new prices. They include a complementary donkey ride (don't waste your time - it's short and you'll be badgered for tips). The prices are about 50 JD for a day 55 for two days and 60 for a three day pass. Exchange rate to U.S. dollars makes it comparable to paying for Disney land, same goes with food and drink and rides inside (As for a complimentary donkey ride? They didn't say anything about that! It was for pay).
  8. Dinner near the hostel - expect to pay from 5-8 JD for an ok meal.
  9. Taxi back from Wadi Musa to Aqaba (arranged by Naser, the hostel owner) - 35 JD 
  10. Jordan departure tax - 5 JD.