Modern, buzzy Amman does a better job than Damascus or Jerusalem of hiding its ancient origins, but Philadelphia (to give the city its original Roman name) does have some notable antiquities.
Foremost among them is the Amman Citadel, built on the summit of Jebel al-Qala'a, the highest of Amman’s seven hills. It has had an extraordinarily long life as a fortress, with evidence of Bronze Age usage, while the remnants of a Roman site, including the Temple of Hercules, are still very much in evidence. This Citadel has also been a royal residence, as indicated by the ruins of the 8th century Ummayad palace, with its largely intact domed audience hall built on the site of a Byzantine basilica.
The Citadel makes a great vantage point over the rest of the city, an especially impressive sight at sunset or at evening as the lights twinkle on Amman’s sloping hills.
The best option for reaching the top of Jebel al-Qala'a from central Amman is to take a taxi; you can always walk down again.