The area around the Cathedral is quite chilled out, obviously you should see Church of the Sacred Family (Templo Expiatorio de la Sagrada Familia) which is the Gaudi church type place, Parc Guell is good for the views of the city, The Olympic stadium is worth a look especially the massive fountain (La Fontana Magica?)on the walk back to the city at night is amazing. It just a cool city to walk about in and going from bar to bar taking life easy.