Madrid Cathedral Restaurant
Normally when you go to a new city, by default you hang in the city centre. So when you get to Madrid, you will probably be walking in and out of Sol and Gran Via the first day you arrive. The first day is also when you are most keen to try local foods and might find it annoying to only see restaurants that cater to tourists -- which means they are expensive, and probably not the "real" thing.
However, if in Madrid, I have good news for you! There is a restaurant called "Restaurante Catedral" on Carrera San Jeronimo 16 -- bang in Madrid's city centre. It does cater to tourists (the waiters kind of speak English), but it is visited by locals as well. It's a large place that has a great variety of tapas in various portion sizes and is reasonably priced, and even serves a menu of the day on weekends -- something not common in other places. It's decor is like a cathedral which makes it an interesting ambiance.
So if you have just arrived and don't want to hunt for something off the map, yet have good, well-priced local food -- you will not be disappointed here. Also, you will always get a table!
Closest metro: Sol
Address: Carrera San Jerónimo 16,
Tel: 91 523 35 56