The downtown of Madrid is full of very original places. The small streets of "Barrio de las Letras" for instance hides a very original architecture with it´s small buildings, old bars and restaurants. Of course there are much more things like the Royal Palace and Plaza Mayor that are almost mandatory places to take a good picture. I also recommend the Temple of Debod and Retiro Park as well. Best thing is that you can visit all these places just during a morning walk.