A great place to eat for a daily menu for less than 10 euros is http://www.gurumadrid.es/

If you want something more typically Spanish, try Spanish omelette with Brava Sauce (slightly spicy) http://www.lasbravas.com/donde_en.html and any of the Museo del Jamón for typical Spanish ham (http://www.museodeljamon.es/). All are cheap and yummy!