The Cosmopolitan is a great place to stay if you are looking to be out and about exploring Madrid. It is close to the Royal Palace and Plaza Mayor. It has a ton of great restaurants and tapas places near by. The Convent for the famous Madrid "nun-cookies" is 5 minutes walk away.
The down side is that it is small, smaller than an average hotel room. And it is not that comfortable... the bed is a Murphy Bed, and is hard... and your pillows will get wedged behind the bed. There is no really comfortable place to sit. But the terrace is a great place to listen to and enjoy the life of Madrid.
As a host Adan is phenomenal. He took good care of us. We recommend the Cosmopolitan especially for a single person.