You should visit:
El Retiro Park: where you'll find lakes, palaces(there's a beautiful crystal palace, see it in the photo at the left handside), etc.
The museums.
The Royal Palace of 'Oriente': itīs possible to visit it within and itīs really beautiful.
If you have time enough you can visit Toledo, incredible city in the south of Madrid with lots of ancient buildings
from several centuries ago.

