Hi Denise, If you are still looking for suggestions, at this moment there are some good deals to be had.
I've stayed in the Zenit
which is a comfortable modern hotel although a fifteen to twenty minute walk to the cathedral, but with a good price per night of 54 € room only.
One that I have heard good things about is Hotel del Pintor
which is right in the heart of the attractions of the city. Currently 60 € a night, again room only. Breakfast tends to be around ten to fifteen euros at most of these hotels but you can stroll to any bar and have a great Spanish style breakfast for a few euros, so I am quoting rates without it.
I have stayed also at the Venecia
, 65 € per room per night, which has the advantage that not only is it in the Alameda opposite Calle Larios , but also there is a bus stop right across from the hotel that goes direct to airport for something like one euro.
Finally, one that caught my eye is the Tryp Alameda
which is where Real Madrid stay when they are in town and that is going for a measly 62 € a night for your dates in September.