The Bébé Cafe is in a niche off the Old Town Plaza Vieja. I'm mostly there for coffee and pastry in the morning, but they also have some great lunch-time sandwiches, and none of the tourist kitsch of most of the eateries in the neighborhood.
For a substantial breakfast or lunch, the Cafe Lush is hard to beat. Close to the center of town, but remarkably quiet and relaxing at the sidewalk tables.
