Hit the Prado if you’ve never been and are vaguely into art. Maybe even if you aren’t. Their Goya collection is the best on Earth. The Prado is right next to Buen Retiro which is also great.

The Reina Sofia is also supposed to be good, but I haven’t been.

The Palacio Real is probably skippable if you’ve been to other palaces. A lot of people will tell you that Plaza Mayor is great. It was ok. I preferred the people watching at Puerta del Sol.

Tapas is everywhere. Which is good. I don’t know where the shopping is, but you can shop at home. Or do I show my could-care-less-about-shopping bias?

Toledo is a quick bus ride away, but given how little time you’ll be in Madrid I don’t know if I’d bother. Nice place, but in hindsight I should’ve spent more time in Madrid.

Here’s a woefully incomplete list of places:

http://www.43places.com/lists/67833/everybody-hates-a-tourist-madrid

Please add to it when you get back.

Hello!Madrid is a very nice city with a great history!I think the best thing for you is to get a tour guide who can help you visit the best locations in the city.Here is the site http://www.localguiding.com/ .I hope it will help you .Cheers!