Now, by violence I mean mostly all things stemming from drug-trafficking (hitmen, kidnappings, racketeering, extortion, carjacking) most commonly found in central america but expanding to southern countries more and more. The safest cities were historically Montevideo in Uruguay and Santiago in Chile, I may be biased but I think Montevideo is still safe and I'm not sure about Santiago, unless you choose to live in the eastern side of the city [0]. EDIT: you may want to factor political instability in your decision. I encourage you to ask other expats about their experience and what they see in the future, they're well-off so they they're lucky to avoid unpleasant experiences the local population has to deal with (plus they can always return to the US). I personally would only live in Chile and Uruguay, so take what I say with a grain of salt.
[0] https://en.wikipedia.org/wiki/Northeastern_zone_of_Santiago