Madrid is a magic city : every night, people meet in the streets, go to numerous sidewalk cafés, café-bars and restaurants in the area of La Puerta del Sol.
Madrileños often walk along the avenues in the evenings when the city's many fountains are illuminated, although this activity has declined as many boulevards have become more crowded with cars.
To have a drink, the Libertad 8 (Calle... Libertad 8) deserves a look : small nice and quiet café, it often welcomes cuentacuentos (story tellers) and cantautores... If you prefer flamenco, go near Calle de los Cuchilleros à La Guitarra.
To eat cheap, cervecería Cien Montaditos, calle Mayor, sells excellent bocadillos (sandwiches) for 1€ (however you will have several to fill your stomac).