I spent two days in Hostal Mesones because of a conference at the University of Granada. The single room was clean and it had a washbasin and air conditioner. I took a room with shared bathroom and it was clean all the time I used it. The owners have recently changed and the new ones are very gentle and provide you with useful information. They speak fluent Spanish, English and French (maybe other languages as well). They have introduced a breakfast of orange juice, coffee and toasts with jam, all included in the price.
During the night the streets are loud but it is solved closing the windows.
If I come back to Granada I will go to Hostal Mesones again.