Sarrià was a village in the hills above Barcelona until 1921, when the city annexed it against its will — the last town to be swallowed, and the one that has stayed most stubbornly itself. Up here, above the traffic, the streets still behave like a place that knows everyone.
Start in Plaça de Sarrià, under the arcades, in front of the Sant Vicenç church; have your coffee while the square does its quiet morning business. Then walk up Carrer Major de Sarrià, the old high street — shopfronts, a market hall, a bakery that has seen out three economies. Stop at Bar Tomàs for the patatas bravas the rest of the city drives up for; check it's open, order the obvious thing, leave it at that.
Then the climb west to the Reial Monestir de Santa Maria de Pedralbes — Queen Elisenda's monastery of 1327, and its three-storey Gothic cloister, arcade upon arcade around a still garden, the nuns' cells opening off the walks. Almost nobody is there. Stand in the middle of it.
Reina Elisenda, named for the same queen, takes you home in one train.