El Matadero : If you are a creative soul, this is your place. It is a modern art center that always has new expositions, and performances.
You’d find a wide variety of programs depending on your interests: cinema, music, art… There is even space for children and teens. Here is the web page in English. Free entrance.
Madrid Río : another interesting idea is renting a bike (you’d bike renting spots all over Madrid and particularly in Madrid Rio) and go around Manzanares river.
The Adventure Park: if you like sports and adventure, you might like this plan. It is a day trip to Cercedilla (Madrid’s Mountains).
In The Adventure Park where you’ll find the best climbing, and zip lining activities. Best times to go would be summer, early autumn, and late spring.
Las presillas: Natural pools in Rascafría (Madrid’s Mountain) are the best idea if you are a nature lover.
I would choose the mountains in the outskirts, it is better to have a car to reach them: Navacerrada, Sierra de Guadarrama, Cotos, Miraflores, Peñalara…beautiful landscapes, trekking, sky and small towns. People from outside cannot imagine that in an hour from a 5 million city we have so many protected parks, mountains, and rivers.
Another option for outdoorsy people is renting a bike and make the bike ring called “el anillo verde”, that is a bike lane that surrounds the whole city.