Also on Montjuic you can see Calatrava's sculptural telephone mast and the site of the 1992 Summer Olympic Stadium which did so much to put Barcelona on the map. There are fantastic views everywhere you look. Further along is the Fundacio Miro, lunch at the restaurant there (Book in advance).
Getting around on foot is easy or you can sign up to the Bicing bicycle hire system. Taxis are cheap, friendly and numerous. Say Catalan 'Bon dia' as a greeting and they'll be even more friendly. Alternatively you can buy a 10 journey "carnet" T-10 ticket at any metro station its the best value and works on buses as well. The metro service is very efficient and air conditioned but when you land take the aerobus from right outside the airport terminals to Plaza Catalunya via the plaza Espanya it costs a fraction of the taxi fare!