Have a look around Plaza Mayor and Plaza Santa Ana, but don’t eat or drink there, for eats, drinks and a bit of nightlife head up to Plaza Dos de Mayo.
Other touristy things and the three main Art Galleries, don’t forget to pop into Atocha Station, across the road from Reina Sofia, to see what they’ve done with the old station and also spend five minutes in the memorial to 11-M, from Atocha you could have a wander through El Buen Retiro.
Madrid is quite small so it’s easy to get around but also the metro is excellent and cheap, get yourself a 10 trip ticket that allows you to travel on buses and metro, it’s about 10 or 11,00€ or even one of these.
These’s a ciclocross race up in San Sebastian de los Reyes on 5th in the morning, go and see the best of Madrid (It’s near the Polideportivo).
A lot depends on what you’re into.
In the area around Calle Cava Baja and Calle de la Cava Alta is supposed to be quite funky and you might find a Flamenco bar or two.
The area around Chueca is very lively with lots of bars and clubs, Chueca is generally considered the gay area but I don’t think it’s contageous so you’ll be ok…
Santiago Bernabeau museum.
Get on a 191 bus and spend a couple of hours in Buitrago de Lozoya and enjoy the scenery of the Sierra Norte de Madrid.
Lots of theatres and or the opera, which reminds me of another eating zone on the Plaza Oriente in front of the Palacio Real. If you’re in that neck of the woods at lunchtime early afternoon pop along to Paseo de Pintor Rosales and enjoy the views of Casa de Campo before catching a late afternoon cable car into said Casa de Campo. as you wander back into town you could pop into Principe Pio Station to have a quick look, not a spectacular as Atocha.
If you’re into the culture stuff get a train to El Escorial or Toledo or Aranjuez.
Or you could just go on the piss for 48 hours. 😀
EDIT: Guernica’s in Reina Sofia, no?