In every part of the city that we have lived, Nuñez, Vicente Lopez (north zone), Caballito, and Palermo, we have seen or heard crime.
One day I was walking in Nuñez on Cabildo right near the Congreso subte stop, and I saw two big burly guys running down the street with a backpack screaming back at some guy. 30 seconds later I saw a middle aged man walking in the same direction that was mugged by them with a lot of bleeding from his mouth.
In Vicente Lopez, even though we lived right across the street from the police, there were several robberies nearby. Granted, we were near the train station.
In Caballito there was a big brawl outside in the street at 2 am.
Our first night in the apartment in Palermo, we had the windows open and heard two very distinct gunshots followed by sirens a few minutes later, and we were 2 blocks from the police station.
A lot of the crime here is a matter of timing. One night we were on a bus late at night and my wife overheard a guy talking on his phone telling his buddies to get ready because he's got two gringos for them to come rob as soon as we get off the bus. Needless to say we got out as soon as we could and took a taxi.
My wife almost had her bag stolen from her in the downtown (while she was pregnant no less). I was pick pocketed in Recoleta.
If you use common sense, most of the time you can avoid having anything happen to you. But sometimes you just end up in the wrong place at the wrong time.
I would still choose any of the areas I mentioned over Villa Soldati or Lugano.