Oh, and if you want 2nd-hand books check out http://www.bookstoreguide.org/2008/02/petras-international-bookshop.html which isn't far from where you'll be staying. Forgot to mention, the cathedral (http://en.wikipedia.org/wiki/Almudena_Cathedral), which is located right next to the Royal Palace, is well worth visiting, and also the crypt right below (going round the corner, you access it via the Cuesta de la Vega, on the corner). The Cathedral I think is free, and the Crypt is about one Euro; most of Madrid's 19th century nobility is buried there, as are a couple of princes. Sadly, most royals are buried outside the city in the Monastery of El Escorial (http://en.wikipedia.org/wiki/El_Escorial) and we won't be able to visit it.
On a sadder note, if you want to see the Monument to the victims of the Al-Qaeda attacks of 2004 it's at Atocha Railway Station (http://en.wikipedia.org/wiki/Estaci%C3%B3n_de_Atocha); there is a plaque in their memory on the main façade of the main building in Puerta del Sol (see previous comment).

Love.