from museums to the famous "tapas" restaurants you have all kind of options.
In the museums you'll find huge original master pieces from Diego de velazques to Picasso, each of the art rooms would be full-field with magical historic paintings and some of them very characteristic of spain.
If you like shopping you may like to go to El Corte Ingles where you will find the "fashion tops" of this season.
anyway barcelona is a place where you have the best of the two worlds (food&culture).