I'm not quite sure this fits into your dining concept but I've always very much enjoyed a place called Cerveceria Santa Barbara. This is a seafood bar which serves a wonderful selection of seafood. Some of the items they carry are;
Gambas a la plancha (sautéed shrimps with sea salt)
Mojama – air-dried tuna (like jam)
Patatas Fritas (quality potato chips)
Berberechos - cockles in a brine with vinegar
Cigalas (cooked Dublin Bay Prawns - some call them French Langoustines)
This place is a great pre- dinner or lunch stopover for a quick local beer (Cruz Blanca), excellent seafood and wonderful potato chips. Santa Barbara has always been a must stop for me while in Madrid.
Plaza de Santa Barbara, 8, Madrid 28004 • 91-3190-4049