Amman has some pretty cheap places that you can stay in which offer good services for a good price.
Jordan Tower Hotel
This hotel is located in the center of Downtown Amman and it is very easy to find. It has been recently renovated and if offers shared dorms and private rooms as well. The rooms are pretty bright and have a TV; the bathrooms are a little bit small. The hotel has a big, bright and warm lounge area and a rooftop restaurant from where you can see the Roman Theatre and the Citadel. It offers free wi-fi and a free breakfast. It also organizes daily trips to the Dead Sea, Petra, and other famous tourist attractions.
This hotel is located near the King Abdullah Mosque and it is a great place to stay in. The rooms have been renovated and all of them have a private bathroom; some of them also have private balconies. The hotel offers other services as well, such as free wi-fi and a restaurant where you get free breakfast. The hotel also has a comprehensive transport service with drivers who speak English.
This hotel is located in Downtown Amman, very near to Jabal al-Qal'a and the Rainbow Street. The rooms have a small seating area, a minibar, air-conditioning and a TV. The hotel also has a restaurant where you can enjoy the traditional Jordan cuisine. Many attractions are at a walking distance from the hotel.