Loads of thieves in madrid- I saw a horrible violent street robbery (much blood!) there, so be aware.
Go to the Prado, and plan for about three hours there. It is the most incredible museum I have ever visited.
The Park near the Prado is a nice walk.
From the prado to the Royal Palace is a longish walk that goes through the plaza major and the other big square.
Loads of dodgy chica bars in madrid- avoid these!
If you get a longer train journey, you need a passport or photo ID.
If you can, day trip to Salamanca on the train. Salamanca is awesome. I think it's about 90 minutes each way.
El Escorial is an easy day trip (90 mins each way?), and the Palace is fantastic. The Spanish civil war memorial is around 30 euros taxi (each way) from el escorual train station- do NOT cheap out and get the bus, or you'll have a LONG walk from the gates.
Segovia is 30 mins by train, but is pretty much just a big roman aqueduct.
Avila is a beautiful walled city, and the train ride goes through the mountains. It's around 90 minutes each way.
Gonna do Rayo Vallecano!