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.
This is a fabulous Hotel called Silken Puerta América, where each floor is designed by a different architect. It is open for public visiting. This year the Hotel was hosting the art fair Just Madrid and I was totally amazed by the first floor design of my favorite architect Zaha Hadid.
A bar and bookshop to enjoy a glass of wine while reading a book or to read a book while drinking a glass of wine. They show a careful selection of contemporary literature and artworks downstairs, from where you can spy on the people upstairs because the ceiling is made of glass.
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.