If you take the train from Madrid to Segovia, Avila, or Salamanca, keep your eyes open as you leave Madrid. About ten minutes from Chamartin station starts the park of El Pardo, previously a royal park. It may not look like much - scrubby little trees, arid soil - but there are amazing numbers of deer in the park; I saw five heavily-antlered stags lying down for a siesta, and deer wading in the shallows of a stream.
I was also lucky enough to be in Atocha station on a day when Renfe was giving out little booklets on bike and hiking routes on the 'Cercanias' (commuter) network. Unfortunately I can't find them on the Renfe web site but I did find some walking routes from Barcelona. And then some more.