If you're just visiting in Madrid (or, if you're a local without a car), the Maciza de Peñalara National Park is perhaps the best hiking area you can find. You can get there on the Cercanias line to Cercedilla (leaving from Nuevos Ministerios) and then you catch an old-school nature train up the mountain to the park. You have you buy your nature-train tickets at Nuevos Ministerios because the train only has a couple of cars and it fills up quickly.
Once you arrive, it's like being a million miles from the dry, urban streets of Madrid. If you go in May and April, you'll still be in time to have snow-covered peaks and trails and plenty of ponds and waterfalls. Your best plan (if you're of average ability and not looking to wear yourself out) is to take the trail towards the glacial lagoon (trail 3). It's a more-or-less flat trail that leads to a lovely lagoon surrounded by absolutely spectacular snow-covered bluffs. The whole thing is quite epic. Luckily, the trails aren't too crowded and, while you'll probably never be the only person in eyesight, you can still go at your own pace without any noise excepts the trickling brooks and chirping birds. It's amazing. Just go!
One of the most important monuments and attractions in Rascafría is the Monastery of El Paular, known both in Madrid and internationally. The Royal Monastery of Santa Maria de El Paular was, for 450 years, a Carthusian monastery, but today it's a Benedictine abbey and the monks continue to occupy part of it. It is, without a doubt, one of the main things to see in Rascafría and should definitely be on your list of stuff to do in Rascafría. Every day, and especially on weekends, tourists come from all over Spain to enjoy this, one the best Rascafría attractions. In addition, nearby is another of the many things to see in Rascafría, the Giner Arboretum and the Bridge of Forgiveness, built in the eighteenth century over the course of the Lozoya River. Other monuments and places to visit in Rascafría are the Antigua Casa de Postas, the Church of St. Andrew the Apostle from the fifteenth century, and the Casona, a set of buildings from the fourteenth century located near the church. In addition, there are many things to do in Rascafria, especially relating to sports. In the municipality there are the ski resorts of Valcotos and Valdesquí, ideal for skiing and spending a fun day. In minube you can look for what to do in Rascafría today to find great organized Rascafría activities that you can enjoy any weekend.