Dear Mai and Ramiro,
Best of Madrid is for you two to enjoy your upcoming trip to Spain. I was euphoric to hear about your plans and decided to contribute. I know it is not your first time in the city, so there are plenty of things you have already seen or places you’ve been to. Therefore I will concentrate on new tips.
The triptych of museums along Paseo de la Castellana is always a must. The Thyssen-Bornemisza Museum, the Prado Museum, and the Museo Nacional Centro de Arte Reina Sofía are unmissable. I would add two more: the CaixaForum Madrid and the La Casa Encendida. Moreover, still in the hood, there is a tiny street behind the Reina Sofía called Calle Doctor Fourquet which is filled on both sides with art galleries. Since we are talking about culture, there is another place worth a visit called Matadero Madrid, for cutting-edge contemporary art.
I am not sure where you are staying, but there are two hotels I would recommend even for a visit to the bar. The Principal in Chueca and the 7 Islas Hotel in Malasaña. My favorite one is Hotel Urso, but a bit on the expensive side (perhaps will save to go with my parents).
When it comes to eating, Madrid is a feast. I love to just walk into any of the bars, ask for a tapa de jamón ibérico and a glass of red Rioja or Ribera del Duero wine. If you find on any wine list the exquisite Pago de Los Capelanes, have at least a glass, if possible a bottle, please. For out-of-this-world tapas, head to Bocaíto (heard Almodóvar is a fan).
There is a place called Platea. It is an old theater transformed into a gastronomic and entertainment center. Lots of food there and a bit on the touristy side. Celso y Manolo is a simple tasca my parents enjoyed. Casa Fidel is always a good idea, especially for brunch, but I would do brunch at Lady Madonna. For an outstanding meal book a table at Ten con Ten. Save space for a coffee at Toma Café, at any time of the day. If cocina madrileña is what you want, the very castizo Malacatín oozes tradition.
There are three essential food markets in the city with plenty of eating options. They are Mercado de San Ildefonso in Malasaña (my favorite), Mercado de Antón Martín in Lavapiés and Mercado de San Antón in Chueca.
As for shopping (even though I know you are not going there for this) you have at least to have a look at some home design places such as Modernario and the atelier of Javier S Medina. The hip concept store Isolée has been on the Madrid scene for a long time, much like Colette in Paris, so a peek is always good.
Since Ramiro is a musician, put on your to-do-list a visit to El Corral de la Morería for some flamenco, though you may save it for Andalucía. The Microteatro Por Dinero is a very creative invention with short plays where the audience is almost part of it. I am dying to check it out. Boguí Jazz and Café Berlín will conquer his heart.
All in all, my favorite pastime in Madrid is to walk and walk and walk. This is how I discover the small bookshops, the independent cafés, and little corners so typically Spanish. Enjoy your time in the city and bring me some fresh tips for TravelVince.
Ps: once in Spain, go to any kiosk that sells newspapers and magazines and buy a copy of the Tapas Magazine guide to eating and drinking in Spain. It is a treasure trove of information.