Will you get any free time during the day? If you do, go to the best art gallery in the entire world- El Prado. Even if you don't think you're into art. It's tremendous.
On a night have a wander around the Plaza's; there are bars down the streets running off each one where you can get a beer and where they bring tapas (a tapa?) free of charge (usually).
It's a surprisingly small city, but lovely all the same.
Stop associating yourselves with astronauts.