We didn't care too much for Amman. It's big and dirty and we didn't find anything interesting to see. There's a Roman theater in nicely restored condition, but we've seen more than our share by now. Our vote: skip it and start in Madaba instead. We didn't actually get to Madaba, but other travelers find it a good place to use a base for visiting the Dead Sea and King's Highway.
The Dead Sea is cool. We did all kinds of great tricks in the water before Steve finally went overboard and dunked his head. That's not good, but it's a lot of fun if you keep your head above water. We went from the showers on the beach to a couple crusader castles along the King's Highway before reaching Petra.
Petra is more than we expected. The famous tombs are just as you do expect, but there is just so much more. We did three days of wandering around the nooks and crannies that most people never see and even had a chance to see the Treasury at night by candle and moonlight.
We hadn't seen enough desert (hah!), so we spent a couple nights in the sands of Wadi Rum near the Saudi Arabian border. Did a bit of exploring, a little hiking and even learned to actually drive our camels. Not a valuable lesson as I never want to sit on one again!
Here's the up and coming beach frontier of Jordan. It's just missing the tourists. We stopped just long enough to get a few dives in to see a wreck along with some of the healthiest coral and definitely most exotic fish in our experience.