During my first visit in Jordan, I went to the citadel. From the top of the hill where it's located, you can see the huge Jordanian flag and that's how your visit starts. A short walk takes you to the Temple of Herod, the Umayyad palace, and the Temple of Hercules, and ends up by the Archaeological museum. It's a wonder not to be missed. My advice is to see Amman at the beginning of your trip, since the rest is even more surprising yet.