Il La Latina neighborhood it is one of the more districts ancient of Madrid, perfect place to have an aperitif. Here is a road, Cava Baja, which offers many clubs and taverns where you can get something to drink. Among these certainly Lamiak or El Tomas where you can also eat something tasty, strictly at the counter.
Le beers are less than 3 € and fun is guaranteed. As you well know the Spanish timetables they are quite different from the Italian ones and if you want to be here in the middle of the party do not show up before 20/21, only afterwards you will think about dinner.
Doing all the way to the end, between one room and another you will arrive up to Plaza Mayor. What is certain is that if you do all the clubs, one by one, in Plaza Mayor you will not get there just give yourself an upper limit that the Madrid night is long;)