You can find information for yourself about the typical places like Museo del Parado, Puerta del Sol or Parque del Retiro, but there is a very nice park, known as Parque del Capricho, unknown for many people that is worth a visit. Right now you is possible to arrive by metro. I think that it is only open during weekends. You can find more information in the link
http://www.esmadrid.com/es/portal.do?TR=C&IDR=877 about 7 years ago
I used to spend childhood summers there and always remember the Estadio Bernabeo where Real Madrid play. If yo are there when is a match is on, definitely go to that, otherwise take a saunter to it and if they allow people in for a look around in the off-season, that would be a treat.
If it is hot, and you fancy a swim and a day out with the locals, look at the municipal pool clubs that team with locals. Pack towels, empanadas, chorizo, fresh bread, tortilla espanola; enjoy your picnic lunch with a sangria that most places serve in their refreshments stands/comedores and you're golden! here's a list to start with, I went to Casa de Campo as a child:
El Escorial is also well worth the trip just outside of Madrid. about 7 years ago