I've done some biking in Cercedilla and Navecerrada which was quite good. You can ride up to the 'puerto' for a challenging route. I also have a book that gives 52 cycling routes around madrid (one for each week of the year). It is arranged by season and difficulty; if you'd like, I could scan you some pages.
I shipped my bike to Spain by air and had no diffuclties (except being overcharged by the taxi to Madrid; didn't argue, couldn't have done it myself)! Take some tools with you and ride to Madrid from the airport, it would certainly make for an interesting intro to Spain!