We stayed at an H10 hotel on Gran Via, one of the main streets which gave us a cool perspective from our balcony.

Down the street is the Plaza de Cibeles, with a beautiful building- the old post office and Mayor's office. A famous fountain is in the plaza, the fountain of Cybele, who is the Phrygian goddess of fertility, on a chariot pulled by two lions.  The Prado Museum is just south of here.

We wandered around and headed toward the Puerta del Sol, a square (under construction so no interesting pictures) which is the "zero point" for distance measurement within Spain.  Nearby we come across the Museo de Jamon, or Museum of ham.  It's essentially a tapas bar coupled with a market.  We're big fans of the spiced, cured meats, and Spain has that in plenty. Unfortunately you can't bring the ham into the US, but you can eat it there... 

So we did, many varieties.  Oh, so good.  At this restaurant, La Taverna La Fragua de Vulcan, a person cut it off the shank in front of you, slowly and carefully, almost religiously.

On our way to the Metro to go to a bullfight, we walked through a large park- the Parque Del Retiro.  Huge and immaculately maintained, it was a very popular place on this beautiful Sunday in May.

This lake is part of the park.

Taking the Metro to the bullfight.  It's well organized and clean.

The bullfight is covered separately.  On another day we went to the Prado, where you are not supposed to take pictures, but which is well documented on their website and Wikipedia
In researching our trip, I found that one of my favorite works is there, the Garden of Earthly Delights, by Hieronymus Bosch.  I was thrilled to be able to see it up close:
From Wikipedia

We enjoyed our two full days in Madrid, but we wanted to spend more time in Barcelona on this trip, which is why this is sort of short.