Madrid, Spanish capitol since 1562, is the geographic centre of the Iberic Peninsula. It's height, and the fact of being over a plateau and surrounded by mountains defines its weather with warm summers and not so cold winters.
As a capitol, it is a very monumental city, with a very popular hearth centre built during the Habsburg reign. The Prado Museum is considered one of the best galleries all over the world.
But Madrid is also a city that never sleeps. It has a huge amount of bars, cafes, theatres, discos which open literally all night. Therefore, do not be surprised if you get caught at a traffic jam at 4am in the night.
Here are some useful links to get you started: