About 6 months ago I had the opportunity to visit a good fried of mine in Madrid. He had lived there for almost 5 years and this was my second trip to La Madre Patria.
If you know locals and wish to have a taste of Madrid in a night try "irse de marcha". There's not an exact translation for this but it basically means go out, hang out with friends, try some local dishes and grab some drinks.
La Venta El Buscón is a really nice place to go and eat or just dring a beer after a hard day. Normally this places have their own wines and liquors available for their customers.
Try some tapas made of different cheeses, meats and vegetables curated in vinegar. "Marcha" allows you to drink a beer in one place and jump from bar to bar or table to table trying the site that best fits your mood.