Reina Sofia museum is always a good idea. And it's never enough of Picasso's Guernica as well as the other modern art gems. Save some hours for visiting and then look round the corner and have some wine at NuBel.
Good place to go for a quick healthy lunch or dinner, you can choose from a variety of paleo, vegan and vegetarian dishes. They also have a great organic coffee too!
Going out in Chueca, the gay neighborhood of Madrid and grab a beer in the bars around is fun. One of my favorite programs is going to tranvestite´s concerts there.
Spanish artist Jaime Hayon is sometimes called Almodóvar of design. So if you like "Kika", colours, Spanish culture and dreamy aestetics, you must visit Barceló Torre de Madrid and stay there for a night or just have a drink in a golden bar.