It's safe ..... but just be aware in Spain, in particular Barcelona, and in very particular Ramblas ....... that there is an increasing frequency of snatches and the "bird poo" scam where you're squirted with something like yoghurt and people come and help by patting you down .....
No personal safety issues .. just if it happens you push people very firmly away that come to help and makes some noise and you will be fine. As with all prudent travel - keep excess cash to the minimum. Leave the passport in the safe but keep a photocopy with you and don't look too affluent!
For what it's worth ... I know NY is safer these days but I feel a whole lot safer in pretty much anywhere in europe than many places state-side!