It's easy to forget that Amman is an ancient city, settled for thousands of years. When it was capital of the Ammonite civilization it was known as Rabbath Ammon. During the Greek and Roman eras it was called Philadelphia, the city of brotherly love. It was ruled by a succession of the Middle East's great empires. For most of that history, development was centered on the Citadel, located on top of a hill in Downtown opposite the Roman Amphitheater.
The first building you'll probably see is the Temple of Hercules, also called the Great Temple of Amman. Built between 161AD and 180AD. All that remains are some columns and the foundation. There are remnants of a Byzantine basilica, constructed sometime in the fifth or sixth century. You can still see the remnants of its mosaic floors. The most intact remains are from an Umayyad Palace and mosque. The wooden dome has been reconstructed.
The view from the Citadel is absolutely breathtaking. Amman's unmistakeable low-rise limestone buildings stretch as far as the eye can see. The Citadel is also home to the National Archaeological Museum of Jordan. The museum is small, disorganized, and the labels are not very informative. Still, it's charming and there are a lot of cool objects on display. The highlight is definitely the Dead Sea Scrolls.
The Citadel is easily accessible by taxi, and within walking distance of Downtown. Be sure to get dropped off at the top of the hill to avoid making the steep climb. Come here first and then walk down the hill to see the Amphitheater. A visit to the Citadel is definitely a must.
National Archaeological Museum
Location: Citadel Hill (Jebel Al Qala'a)
Telephone: +966 6 463 8795
Hours: Open daily 09:00-17:00 (winter); 09:00-19:00 (summer); 10:00-18:00 (Fridays and holidays)
Admission: Admission charge.