Petra

From Amman, the cheapest way to get to Petra is by bus (JETT bus is about 10 JD/person each way). Otherwise, consider combining a Petra trip with a Wadi Rum or Aqaba trip, since all are South of Amman. Taxi is also an option, and can be equally cheap depending on the deal you strike.

Petra is a massive city carved out of mountains and one of the seven wonders of the modern world. For the full experience, make sure to see:

• The Treasury (near the entrance, famous picture. It is illegal and dangerous, but you can stike a deal with the many vendors/guides to take you to the top of a nearby peak for an even better view of the Treasury. If you do this, make sure to clearly negotiate a price before ascending.)
• Wadi Musa (sandstone rock canyon that served as a waterway for the Nabataeans.)
• The Monastery (~1.5 hour uphill hike, equally striking. The locals call it the "best view in Jordan")

Petra is very touristy with many vendors selling trinkets, tours, and animal rides. You can partake, but beware that tips are expected for most services, and the Bedouins will be aggressive in trying to get you to buy their wares. Be mindful also of standing out too much — it is easy to get ripped off, and they are looking for people who seem cluless. Act purposefully and be firm when negotiating.