The sprawling capital of Jordan undulates over seven hills, and is home to more than a million people, making it larger than any of Israel's cities. There is an older "downtown" area around the ancient, beautifully restored Roman Amphitheater, but there is no one main business center or hotel district in Amman. Offices and hotels are scattered randomly across the entire sprawling city.
In biblical times, Amman was Rabbath-Ammon, the capital of the Ammonite people; in the Hellenistic/Roman period, this was the formidable city of Philadelphia, a member of the league of cities known as the Decapolis -- impressive ruins from those times still blend into the structure of modern Amman. During the early 1920s, when Trans-Jordan was carved out of the wreckage of the Ottoman Empire, centrally located in Amman (at that time little more than a village), rather than the larger town of Salt to the north, was chosen as Emir Abdullah's administrative center. Until 1948, Amman remained essentially a small town with a population of less than 12,000. Palestinian refugees from the 1948 war swelled the city's population; like the rest of the country, more than half the inhabitants of Amman are of Palestinian origin.
The city is an interesting, lively base for exploring northern and central Jordan. Independent travelers will, of necessity, spend time here making touring arrangements. Amman has fabulous (and very affordable) Middle Eastern restaurants as well as interesting local craft cooperatives and shops to visit. A walk or drive through the residential areas of Abdoun, not far from the American Embassy, reveals street after street of new and under construction stone mansions and villas; some are garish and flashy, but you'll also see many examples of interesting, exciting modern design.