The town of Azraq is not particularly attractive but it does house an interesting fortress - the Qasr al-Azraq Castle, where Lawrence of Arabia once stayed. It's a great introduction to the larger castles found further along the route. I really enjoyed the on-site guide's tour - a dynamic presentation of the castle.
I also liked the visit to the Azraq Wetland Reserve on the outskirts of town. It's what's left (15%!) of an oasis that became Amman's main water source... The oasis is no longer being drained, but today you'll find its size has shrunk. There's a short but lovely walk around the large pond, which is bordered by lush plantlife. There's lots of well explained information on the local ecosystem. You'll also spot lots of birds - it's a calming place