If you want to avoid people completely then check out the neighbouring provinces of Soria and Teruel, around half way between Madrid and the Pyrenees. This region is incredibly underpopulated (if you have a kid or two some villages will in effect pay you to move there to keep the schools open!) but has fabulous roads over mountain ranges and through forests. These are also good if you plan some trail riding as there are few nature reserves, in which much off road traffic is banned. There are some camp sites and an impressive lst of farmhouse bed-and-breakfast style accommodation, called Casas Rurales
. The best way for foreigners to access these is via the tourism offices located in all towns and large villages. They will ring around and book for you as you will find that no one else speaks English. You can have half board for a very reasonable price - but be prepared for home cooking - pigs trotters, snails and lots of offal are always a treat for unsuspecting Guirris
For a sense of purpose try riding the length of the Pyrenees, seeking out the routes along to the French border, which runs along the top ridge of the mountains. As a broad guide the area further way from the mountain ridge, the pre-Pyrenees, has the faster roads and in some ways more spectacular scenery, which huge limestone gorges, whereas the higher routes pass through narrow glacial valleys and the riding is often along country lanes - not so much fun on your Ducati 1198 SP, aw shucks, you'll just have to trade it for the new Diavel!
The whole Pyrenean region is developed for mountain tourism, but this is high class, nothing at all like the 'Costas'. The advantage is that accommodadtion, including camp sites, is easy and there are lots of fringe activities like white water rafting and slalom canoeing (the townships of Llavorsi and Sort on the river Noguera Pallaresa in Catalonia are the 'capitals' for these sports), and barranquismo
- the Sierra de Guara in Aragon, more or less half way along the Pyrenees, is the most famous place for this, although the sport is popular throughout Spain - as long as there's some running water in the rivers!
Way over in the west, another good route is to follow the actual Via de la Plata
itself, rather than the main A66 motorway route that is named after it, as Pete mentions above. The route was an ancient trading way dating from pre-Roman times and there are sections of greenway to be explored as well as the possibilty of using secondary roads to link the towns along it - most of which are historical and very lovely, having been left behind since medieval times.
Finally, and this requires some serious research beforehand, why not try devising a route across the Peninsular following the Cañadas Reales
? These are ancient rites of way for nomadic cattle ranchers which retain their status and are still used to this very day. All are supposed to be 150 metres wide to allow for the herds and one passes right through the heart of Madrid! If you run across the herders along the way they might string you along - enjoy!