Madrid is unexpected in its eclecticness. You will find hip areas, protest areas, fake city guides, awesome museums, a lot of green spaces and of course palaces.
Also, its art museums deserve a full day – especially Reina Sofia, which showcases a lot of Picasso.
If you’re not among the weak hearted, be sure to check Corrida des Torros. It’s an architectural marvel and the show is shocking but worthwhile – see here.