Well! DD and I must have been lucky. We had no trouble with thieves or pickpockets when we were there a few weeks ago.
We went to the Gaudi museum and the park up above the city, views beautiful, fountain amazing! And the ex Olympic park while we were up there.
We stayed near the Cathedral Catalonia. Cathedral (withgeese) and whole area round there, is amazing. Very old and atmospheric. Las Ramblas is great for just wandering (and buying tat
)
In fact, I think Barcelona, especially the beautiful Gothic quarter, is made for just wandering, and looking, both by day and night.
Buy tickets in advance for Sagrada Familia. Very long queues to negotiate otherwise.