Petra, the capital of the Nabatean Kingdom dating to 300 BC, is located in Jordan's SW desert between the Red Sea and Dead Sea. Accessed via a narrow canyon called Al Siq, it contains tombs and temples carved into pink sandstone cliffs. The Nabataeans were a wealthy society that dominated the trade network of the frankincense and spice routes covering three continents. It controlled a network of camel caravan routes and checkpoints, and extracted tolls for safe passage as well as commerce.
An incredible area for desert hiking and exploring, it is one of the world's most famous archaeological sites. If it's hot, leave as early as possible (upon opening) with your water and snacks. There are also some small cafes spread around the main trails. The area is huge, some 60 square KM, so you'll need more than one day to see the most important sites.