South Africa (e.g. Western Cape) could also be a nice option if you don't mind the added distance. They offer independent means and pensioner visas. Similar climate to Argentina. Cost of living a bit lower than here, good private education, healthcare and professional services, very nice lifestyle but also not without its short comings (e.g. constant power and water shortages, mismanagement and corruption, insecurity - BUT and it is a big but, safety depends on exactly where you live and go... quite like Argentina actually but with a more open and stable economy where you can find anything you want).
Avoid... like you said with all your negative points. South Africa is dangerous and any cost of living saved is spent trying to top up what the State should, but does not provide. Cost of living is actually far higher in South Africa than Argentina and the state provides very little. There is no or very unreliable public transport unless you count mad minibus taxis. Even Cape Towns city busses while fine dont cover nearly half as much of the city as BA busses do and strikes and public violence render the service unreliable and unsafe. Trains work sometimes but you would never want to go on one as it makes you an easy target for gangs that rob people. I had a friend who lived in Cape Town who would carry a dummy phone to give to the gang members when they used to rob people.
If you live in South Africa the initial investment to simply live is astronomical as you would need independent power supply (solar and inverter), a water well or borehole or at the very least rain tanks and a filtration system (in some places, not all), private security (ADT or the like), electric fencing, private medical, a decent car, a house in a decent neighborhood (you can't, as a foreign person, even begin to think of living in the more unsafe neighborhoods with cheaper houses like you can in Arg).
Additionally, simply getting a visa is going to be almost impossible for atleast 2-3 years. Home Affairs here is impossibly slow even if you are an investor or retiree or getting a work visa.
The economy is stable in that it is not like Argentia or Turkey or Zimbabwe but in reality the country is on the brink. There is definite feeling that things are going to go wrong. There are huge civil and societal issues that have never been dealt with that will eventually explode in South Africa. This next election in May seems like there will be no outright winner so there is likely going to be more instability there.
There are expats that live well but they are used to the place and have adapted and maybe they enjoy this wild west kind of lifestyle... I dunno. If you are rich and can isolate yourself from pretty much everything then there is a life to be had in South Africa in Stellenbosh or Francshoek but at that point just go to the south of Spain or Portugal or Bangkok.
I spend half my time between Arg and South Africa but I would choose every single day to rather be in Argentina 100% of the time.