Climb Montjuic to the National Art Museum of Catalonia, which has a Turner exhibition until 11 September, and wander up Passeig de Gracia to see the extraordinary Gaudí buildings - Casa Batlló has night-time visits which include a rooftop concert - and, of course, the architect’s unfinished masterpiece, the soaring Sagrada Familia (be sure to book tickets in advance).