Hostal Josefina is very centrally located, easy access to a lot of things, close to a metro stop, Puerta del Sol, Plaza Mayor. I have never stayed there so can't tell you any more about it, but I have a friend that lives within 2 blocks of there that I stay with.

I stayed at Hostal Adriano before and loved it (especially if the long awaited elevator is installed!!) A little more than Josefina, but not much.