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.
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.
A piece of Egypt in the city centre. This temple, a gift from the Egyptian government, was taken stone by stone from the valley flooded when the Aswan Dam was built. It’s a great place for a picnic in the summer. You can enjoy the sunset and the (grey) skyline of Madrid.
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!