Barcelona's upper reaches begin with Pedralbes, a neighborhood of graceful mansions grouped around a stunning Gothic monastery. Park Güell is Gaudí's Art Nouveau urban garden. Gràcia and Sarrià were outlying villages swallowed up by the expanding metropolis. Note that the Monestir de Pedralbes closes at 2, so it's a good place to start. Tibidabo, with its amusement park and Norman Foster's Torre de Collserola should be considered only on an (increasingly unusual) unsmoggy day.