The Jordan Museum, located next to the City Hall, is a museum of international standard. Housed in a beautiful modern building, a series of beautifully presented and informative displays tell Jordan's historical epic from the first people through the Nabatean civilisation to the cusp of the modern era. Highlights include the oldest-known human statues (the spookily modern 8000-year-old mannequins of Ain Ghazal), Jordan's share of the Dead Sea scrolls, and a host of remains from Petra and surrounds.
The upstairs galleries, featuring Islamic Jordan to the Arab Revolt, were still to open when we visited, but either way, this museum is a must.