Hello Rozenkratz, here's what I would recommend...
Take the very inexpensive Double-decker buses
MadridVision This will take you up and drop you off at the top tourist sites in the Center of Madrid, El Centro. It offers three tours Madrid Historico, Monumental and Moderno for about 10Euros.
If your time is limited, I would visit the following places.
Museums:
Well to begin you must see at least two Museums: The Prado (Free to the public on Sundays)
The Reina Sofia (Modern Art) Here you'll see Guernica, very impressive!
Palaces:
You must take a peek at the Royal Palace
Parks:
Retiro Park ( parque del Buen Retiro) The Book Fair is going on now near the park and Botanical Gardens
Plazas:
Of course, spend some time at the most beautiful Plaza in Spain: the Plaza Mayor! On Sundays they have a stamp and coin show.
Gateways:
La Puerta Del Sol, always a happening place, see Jer's Webcam. Here you you see the Brear and the Strawberry tree and the Kilometer ) block.
El Rastro: On Sunday this is the biggest flea market in Spain!
Also, if you have time do take a short daytrip to Segovia, it's well worth the time. If you have more time take in Toledo!
There are lots of more places to see! These are just a few of the highlights.
For food and fun I suggest a search of recent posts by returning travelers or by the local Madrile�os.
Buen viaje!
:cheers: