The Anillo Verde is a great way to see Madrid - you can ride the whole way around the city if you like, a total of about 60 km. I think once a month or so there's a group ride of around 200-300 people that do the ride in the middle of the night, and all are welcome (http://www.vueltanocturna.es).
I really enjoy the Anillo, using it both for my morning commute and for weekend workouts. Some suggestions, though, if you want to put in some training miles. Once you get to Casa de Campo, the big park to the west of Palacio Real, you can peel off onto some tracks within the park. There's a goo one for riding interval that goes in kind of a big loop around the lake, climbing up then descending behind it. I'd say that's around 5 miles. But all of this gets pretty busy, and the cyclists become increasingly erratic (basically recreational/families, which is fine, but not good if you're going into a bend at 30+mph), as the day proceeds. As a result, I prefer to get out there early, say 8am, when you'll only see a handful of others. You can also follow the Anillo out to the north of the city and pick up another protected bike route alongside the M607, heading towards the Autonomous University. I'm reliably told (though have not *yet* attempted) that this will take you out towards Tres Campos, where you can hop off the path and head up into the mountains for some serious riding.
Oh, and there are some useful maps here:
https://maps.google.es/maps/ms?ie=UTF8&oe=UTF8&msa=0&msid=101099372197898237033.00044de22e518bf6fccf8&dg=feature
http://www.infobicimadrid.es/gis_bicis.htm read more