Walk over to the Mercado de San Miguel from there (just off Plaza Mayor to the west). They've got maybe 40 food/drink vendors where you can buy pintxos/tapas like croquetas de bacalao (cod), various Spanish cheeses, jamon, wine and desserts, some for as little as 1 euro.
A couple nice places to eat/drink include Mercado de la Reina on Gran Via and Gin Room (drinks of course) just off Parque del Retiro to the west. And of course you're a few minutes walk from the Prado and Reina Sofia museums.