If during your trip to Jordanyou leave Amman and head east, you'll be able to visit the beautiful castles in the region of Azraq. If you have to choose just one, Qusayr Amra has to be it.
When you've yet to plan your trip to Jordan, you'll surely mark visits to the archaeological site of Petra, the Dead Sea and Wadi Rum (the desert) as a priority. It's rarer to schedule a visit east, towards the town of Azraq. There, you'll be in the region of castles, including the very beautiful Qusayr Amra.
Amongst the numerous castles in the region, such as Qasr Al-Kharana, Qasr Al-Mushatta and Qasr Al-Azraq, for example, Qusayr Amra is, without a doubt, the most beautiful. Moreover, it's the only one of them to be classified as a UNESCO World Heritage Site. That shouldn't stop you visiting the others, as the entrance ticket for one opens the doors to all of them.
When visiting the building, you'll surely think that the word "castle" is slightly exaggerated. It was originally a resting place for hunters and it was also used as a hammam. Nowadays, it's mainly interesting to visit because of its state of preservation. At the end of the visit, the small museum houses some very beautiful frescoes.
To locate it geographically, the castle can be found on the road between the capital, Amman and Azraq. Qusayr Amra is 85km from Amman and just 25km from Azraq. It's fairly complicated to get there by bus as none will drop you right in front of the entrance. At best, you'll just be left by the side of the road. In all cases, you'll have to finish the rest of the journey by hitch-hiking. Please be assured that this works very well and you'll have no difficulty in finding a vehicle to take you.
The ideal scenario is to take a taxi or to have your own car. If you're worried about driving yourself, you can always rent a car with a driver, but that soon becomes fairly expensive.