Here's a link to my itinerary from 2 years ago In Madrid.
I stayed at the AC Recoletos both that year and again last year when I visited northwestern Spain. There are photos of my rooms for both years in the thread.
I also stayed at the Recoletos hotel. It is very modern and in a great part of Madrid. Would go to the park right near by and of courser the Prado museum . Just in case you don't know the city has a different schedule than you might have. I had trouble finding a place to have coffee before 9AM and restaurants for dinner get busy around 9PM