There are loads of great walks around this area. If you want to explore the town just set off in any direction and enjoy getting lost in the winding narrow streets. For those more adventurous then why not do one of the many mountain walks, including:
The Revolcadores – here’s a great walk, mapped out for you. Here’s a partial translation of the route: Climb the highest peak of Murcia from Cañada de la Cruz, the ascent begins from the town by an old road that leads us to a farm and a burnt house, to the right of the ravine a magnificent indigenous forest leads without much difficulty and without much slope to the first point, the Revolcadores, at 1999 meters. From here you can see the trig point of los Obispos (the bishops), after a few minutes walk along the plain, we reach the top of Murcia at 2015 meters. For the more adventurous, now set up your climbing ropes and continue, for us mere mortals, just follow your steps back down to Cañada de la Cruz.
Ruta Huerta de Tenorio y Moratalla La Vieja – This walk (or cycle) starts in Moratalla town and heads off into the fertile plains (Huerta), it’s a great circular route to do from the house, but it is a long one. Set off early and take plenty of water. The site has a map and a route description (in Spanish, use google translate if you need it in English), the route is marked along the way with red dashes on rocks and posts.
Ruta urbana y vuelta al Cerro de San Jorge – An easier walk, from town again, you can start at the castle. This is a circular walk, and takes you through the winding streets and then off up to a view point.
If you have a car there are plenty of other great walks, there are some listed on the ayuntamiento site here.
There’s a cycling club, which has routes on it’s website, take a look here.
Take a look at the walking routes above as most of them are modifiable for cycling.
Take a look at Qalat for lots of other activities in the area – including kayaking, rafting, caving, archery and paintballing.
There’s also horse riding, go-karting, golf, clay pigeon shooting…