Madrid became the capital of Spain only in XVI century, when this once powerful empire was already on the decline. That’s why it has the appearance of today megalopolis.
However, there are something to see in the city, for example Plaza Mayor, Royal Palace, Retiro Park, and of course Prado Museum.
When in Madrid you should plan a trip to the suburb of Madrid and visit Escorial. It is one of the largest European palaces, built by Philippe II. Under the reign of this king Escorial was both a monastery and palace, and after his death it was also made the burial place of Spanish monarchs.
Externally, Escorial is but a gloomy castle. It has no fretwork and its windows strongly resemble loopholes. However, inside the palace there stored the huge collection of art work gathered by the kings of Habsburg dynasty (now it is mostly moved to Prado). You should go to the church to see the Altar and Crucifix made by the famous Italian sculptor Benvenuto Cellini.
You must visit Prado Museum, even if you aren’t used to visiting such establishments. Prado is rightly considered one of the best, and possibly the largest, art galleries in the world.
As to historical sites of Madrid, you may start your acquaintance with them from the main city square (Plaza Mayor). The square is surrounded by buildings with towers built in Spanish style. It would be nice to sit at one of the local restaurants eating paella. Nearby there is Retiro Park, where you can have a respite from tiring promenades in the shade of trees. Royal Palace is still the residence of Spanish monarchs, but only for official receptions. Otherwise, it is open for visiting.
From Madrid you can make a trip to the ancient Spanish capital Toledo (it takes 2 hours to get there by train). The city preserved its medieval appearance until nowadays. Also, you may visit some other cities, such as Segovia, Cuenca and Avila. But the se trips would take at least 2-3 days.