Visit Museu Nacional d'Art de Catalunya in Parc de Montjuic. This museum is major depository of Catalan art. It is the most important center for Romanesque art in the world. Highlight of the museum is the collection of murals from various Romanesque churches displayed in apses, much as in the churches in which they were found.
One of the numerous versions and interpretations of Las Meninas by Velasquez. All versions are in one large hall with explanations of how to campare each with the Velasquez painting. Very interesting.
Go to the famous beach-Platja de la Barcelona. You sometimes the Gaudi's crocodile masterpiece by artist.
Its well done and is a real size crocodile!
Keep an eye out for Mies Van der Rohe's famous Barcelona chair, the beach even has Barcelona Benches.
Even though Barcelona in many ways is a modern town, it doesn't look like all areas yet have cable tv.
Barcelona is one of the most interesting cities for lovers of modern art. You´ll need many weeks to discover all.
One of my favorites is the Miró museum