Mapa del delito out...BA Crime Map. Palermo tops the list.

Here's the latest list of crimes committed according to neighborhoods. Palermo tops the list. followed by Recoleta & Caballito.
I live in Constitucion and I have to say I feel very safe. Not too many tourist come here. Maybe that's way.

This article is a bit misleading as it speaks of total crime and not crime adjusted for population. Palermo is the largest barrio in CABA by quite a lot so it stands to reason that there would be more criminal acts in Palermo then say, Coghlan, which as less than 10% the population.

Wikipedia has a breakdown of barrios by population, but the numbers are a bit outdated.
5000 phones are stolen in Argeninta every day. That should tell you something.

However, as far as physical safety goes, and despite sporadic tragic episodes, Buenos Aires isn´t as dangerous as its made out to be. In fact, it has a considerably lower homicide rate than the capital of the country hailed internationally as a model and progressive haven, Uruguay.