Jordan's location in the geographical “near east” has exposed it to dozens of civilizations over the course of history. In the last three thousand years alone the region has invariably fallen under the Persian, Greek, Nabataean, Roman, Byzantine, Arab, and Ottoman empires, the legacies of which are often still visible today.
One prominent example of Amman's Roman legacy is the ruins of the Temple of Hercules atop Jabal Al Qalʿa — the “hill of the castle” (or citadel), one of the city's original seven hills. Towering above the bustling center of downtown Amman, these few surviving pillars are a literal icon of the city. From here you can also see other notable Roman-era sights such as the Theater, Odeon, and Nymphaeum, as well as contemporary landmarks like the Abu Darwish and Husseini mosques.
Other attractions at the citadel include partial remains of the Umayyad Palace and a museum exhibiting artifacts from human activity in the area where you can see tools, pottery, coins, etc dating back to the Iron, Bronze, and Neolithic ages.
I recommend visiting the citadel one hour before sunset when the light becomes a warm, golden orange color. Entrance to the citadel is included in the Jordan Pass, so make sure to bring yours with you if you have one.