The biggest jump on this list, both in distance and in climate: January in Petra typically runs 8 to 15°C, and Wadi Rum 12 to 18°C, cool enough that layers matter in a way they don't anywhere else on this page. Direct flights from Dubai run around 3 hours on Royal Jordanian or flydubai.
Petra
The Nabataean city carved into rose-red sandstone is reached via the Siq, a narrow canyon approach that opens onto the Treasury (Al-Khazneh), the building most people picture when they think of Petra. Beyond it, the site extends much further than a single monument: the Monastery and the High Place of Sacrifice both involve a genuine uphill climb and are better attempted on a second day, once legs from the marathon have had more time to recover. The full site covers a walking distance of around 15 km if the outer monuments are included, which is worth spreading across two visits rather than attempting in one long day.
Wadi Rum
A red sand and granite desert valley roughly two hours south of Petra, reached by 4WD jeep tours or, for the more energetic, by camel. The scale of the place, vast open valleys flanked by sheer rock walls, is the reason to go rather than any single sight within it. An overnight desert camp is the standard way to experience it, with a cold, clear night sky a genuine feature of the stop rather than an incidental one.
Where to Stay
A base in Wadi Musa (the town beside the Petra site) covers the two Petra days, with a desert camp stay in Wadi Rum itself for the extension south. Both are well served by tour operators who can arrange transfers between the two.
Getting Back
Direct flights from Amman back to Dubai run on both Royal Jordanian and flydubai, taking the same roughly 3 hours as the outbound leg. Petra and Wadi Rum are both a drive from Amman, so build a transfer day into either end of the trip rather than a same-day flight connection.