How to spend an afternoon and night in Madrid?

get all of your tours or museums out of the way and start eating jamon (ham) and drink wine! THATS IT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Walking by the central area around Chueca and Centro Comercial Gran Plaza 2, or in the museum area with Museo Nacional Centro de Arte Reina Sofía, Museo Thyssen-Bornemisza and Museo del Prado, all within walking distance, and close late some days in the week.

To have dinner go to Chueca lively neighborhood. 

They sleep during the afternoon, so don't arrive hungry! At night  there's tons to do. Walk around the city and the crowd will lead you ; )

I would just have a walk around the center, going to Plaza Cibeles, Calle Alcala and Plaza del Sol. If you have lots of time you could go to Museo del Prado or Museo Nacional Centro de Arte Reina Sofía.

As for food, there are tons of places. I like Taberna del Chato, or you could try a typical bocadillo de calamares at El Brillante

Hola Yaniv,

There are so many things for you to do! Madrid is so full of life and people are always out late so you're in luck!

If you like museums, you can take advantage of the free hours that are offered.  The Museo del Prado has free hours from 18:00-20:00 and the Museo Nacional Centro de Arte Reina Sofía from 19:00-21:00. You would use metro stop Atocha to get to both of them.  Parque del Retiro is also a good option if after a long flight, you want to walk around for a bit. Sol is the city center and it's very touristy but there's a lot to see and do around there. You have the Plaza Mayor close by, Gran Vía and you can also walk down about 10-15 minutes from there and see the Royal Palace of Madrid.

For tapas, I would head to the neighborhoods of La Latina (metro: la latina) or Malasaña (metro: Tribunal/Bilbao).  They have a lot of good tapas bars and places.  The Mercado de San Miguel (very close to the Plaza Mayor and not far from La Latina) and the Mercado de San Antón (metro: Chueca) are fun places to see different types of tapas and hang out and get a glass of wine or beer. Mercado de San Miguel is older and has that cool European market vibe. Mercada San Anton is a bit more modern and has a really cool rooftop deck.  

I'm not too sure about the music scene.  There's a place in Malasaña called Triskel Tavern that sometimes has live music, but it's more of whoever comes (usually expats) and signs up to do it rather than a specific band that plays there.  In La Latina, you could pay to see a flamenco show and they have some really good ones.  If you've never seen flamenco before, I would definitely recommend it.

Buen viaje!

In the afternoon go to Parque del Retiro. After 5pm maybe too late.