Sultan Hotel is definitely the best budget choice in Damascus. The staff is helpful and speaks English, and the rooms are nice enough. The location could not be better, as it is only a short walking distance to the Old Town and bus station.
Most of the rooms have a bathroom attached ($20), but I chose to stay in a big, quiet room with the bathroom outside on the corridor ($16). The bathroom was just next to my room and shared only with another room (which was unoccupied most of the time), so I found the deal perfect. Especially because there was a balcony in my room!
One can also have a breakfast there and watch television in the comfortable lobby. They have several foreign channels. There are no rooms with television. Internet access is available but quite expensive.