Petra is a city carved into the cliff faces in a series of canyons in the South of the country some 250KM from Amman. It is possible to "do" the ruins in a day, but most people take 2 or 3 and look around them leisurely. There are hotels in Wadi Musa nearby, and the area is developing as a tourist centre.
Petra was built around 2500 years ago by the ancient Nabateaeans as their home. You approach the city through a narrow cleft in the rock, and come face to face with the treasury, or Khazneh, one of the most imposing buildings on the site, and made famous in the Indiana Jones film, The Last Crusade. Nothing prepares you for how impressive the buildings are, and it is easy to lose yourself amongst them for hours.
The desert Castle loop from Amman takes you out into the desert to see a string of impressive fortresses, some from Roman times, but others much older, and like Petra, are attributed to the Nabateaeans. The trip takes around two days by car.
The area of Wadi Rum is to the South of Petra, and is home to some of the most beautiful desert scenery you can imagine. The area was used extensively in the film Lawrence of Arabia, and gazing out over the sands and natural monuments, it is easy to imagine yourself in his sandals.