Caballito is highly recommendable in my opinion. It's beautiful, rather safe, and a lot less expensive and touristy than Recoleta or Palermo. And you have the subte to the center in 10 mins! I couldn't find a place in Caballito so I live in Almagro which is near, and is not bad but is only a bit rougher in some parts at night. But in general Almagro is a nice neighborhood, you get a real neighborhood feel more than some of the more ritzy touristy areas.
Just a question: when you all talk about Abasto and it being dangerous at night, what zone do you actually consider 'Abasto'? Given that it's not a real neighborhood, but rather a made up one around the abasto shopping, I'm curious to know more or less from what street to what street is actually considered Abasto. Thanks!