Very important part of Madrid :-)
Plaza Santa Ana: many tapasbars, from traditional to modern. We recommend "Turf" (yes it is a weird name).
Galician BBQ: behind the momument of Cervantes, extremely delcious and fun.
Mercado: So much food! Try everything!
El Tigre: get free tapas with your drinks, very crowdy but a nice experience.
Cervecerias: found in almost every street, good beer and good tapas.
Bazaar: terrific restaurant! Great food and not expensive.
