The park is lovely! It has a nearby Zoo (Zoo Aquarium de Madrid), Amusement park (Parques…read moreReunidos), and the Madrid Arena. There are plenty of running and biking routes, and lots of nature to explore.
The best part is the Lago de la Casa de Campo, which has several restaurants nearby. The restaurants are overpriced, but still worthwhile for the relaxing outdoor terrace along the lake.
There are three metro stops near by - one by the lake (Lago), Batán, and Casa de Campo, but all are on the periphery of the park, so expect a long walk. You can call a taxi, but there are none waiting in the park.
While in the park, be sure to check out the Teleférico de Madrid, which is a good value at less than €5 for the 15 minute one-way trip, and just over €5 for the 30-minute round trip. The above-ground cable car runs from the middle of Casa de Campo to the Rosaleda de Madrid park near Argüelles.