Hi Kells
If you haven't already booked Carlton. This hotel seems to be in the area you want:
http://es.melia.com/hoteles/espana/madrid/tryp-madrid-atocha-hotel/home.htmBut it only just scrapes into your budget in October.
If you take a look at google maps you can find a large selection of hotels based on area:
http://maps.google.es/maps?q=hoteles&hl=es&ll=40.416796,-3.692479&spn=0.008806,0.019033&sll=40.416796,-3.692479&sspn=0.008806,0.019033&t=m&radius=0.6&hq=hoteles&z=16
I hope that helps.
It'd be easier to find something in your budget if you let us know when you're travelling.