The amphitheater in downtown Amman is the most magnificent remnant of Amman's Roman past. It was built around 170AD at the height of the Roman empire, when Amman was known as Philadelphia. The capacity is upwards of 6,000. Amphitheaters were the heart of Roman civic life. Citizens would gather there to watch plays and discuss politics. The Nymphaeum, an impressive Roman fountain, is also located on site.
This is a must see location. Built into the side of a hill, the amphitheater is very impressive. Climb to the top to get some spectacular views of Amman, though be careful because it's a steep climb and there are no guardrails! Along with the neighboring Odeon, a smaller 500-seat theater next door, the amphitheater still plays host to plays and concerts during the summer. Try to catch a show there if you can -- there's nothing like watching a show in an ancient Roman amphitheater.
Two museums are also on site. The Jordan Folklore Museum has exhibits dedicated to the traditional Bedouin lifestyle of Jordanians. The Museum of Popular Traditions is focused on the decorative arts of Jordan. The collection features traditional dress, embroidery, and jewelry. It also houses an impressive collection of mosaics from around the country. It shouldn't take more than an hour to get through both museums. You may as well stop by since entry to both is included in the cost of admission, and there are some interesting items on display.
Location: Quraysh Street, Downtown
Hours: Museums open Wednesday through Monday 09:00-17:00
Admission: 2JD covers entry to the amphitheater and museums.