Hi Margret,
I would absolutely go to a "neighbourhood" restaurant and get the menu del dia - the daily special that normally contains two courses, bread, beer/wine/water and coffee or desert. It's great value for money, and it's also very typically Spanish. Our favourite lunch place in Madrid is called "Madrid Madriz", and it's just next to metro Tribunal, on c/Fuencarral. It's always packed with locals, has friendly staff, and a nice choice of dishes. The price is 7.50 euros for the menu - you can get cheaper, but I doubt you can get better.
There's another lunch place in Madrid that I've heard about that's supposed to be super, but I haven't tried it. It's just off Gran Via, on c/Caballero de Gracia (or it might be c/de los Jardines, it's one of the two). This area is more known for its prostitutes than its food, but this restaurant is supposed to be very classy, and there is always a crowd outside trying to get in. I think the price for the full daily menu is 10 euros.
I'd recommend that you get to either of these restaurant fairly early, as they tend to fill up quickly and as the Spanish like their long lunches it might take a while for a table to become free...