The Citadel which is the oldest part of Amman and offers a panoramic view of the city from the entrance. I know that you can trace the history of Amman from ruins found here, but to me the park was a collection of pillars and rocks. We saw the remains of the Roman temple of Hercules, but even that is disputed as part of the remnants of the entrance statue is that of a woman’s hand and can also be photographed from the park entrance gates. Get a taxi to the park entrance gates and take the panoramic view and the temple of Hercules and then back in the taxi.
Amman Citadel is only for the real history buffs as most of its treasures are located in other museums. If you do visit ensure its with a guide as the attractions are not signposted.