you found a fucking idiot with mental problems
there are security problems like in every place in the world, but there are certain places that might be dangerous (usually around South and West Buenos Aires suburbs) and most of Argentina is quite safe. More if we're talking about a trip to Las Leņas, your driver really needed some medication!
As for the question from the OP, North suburbs of Buenos Aires are really cool, lots of night life, really cool places, really great to raise a family and so on. And depending on the place, from 30% to 200% more expensive than Buenos Aires city.
You also have the option of La Plata, a rather big yet not a mega city and only 31 miles from Buenos Aires. It's a really beautiful city, a lot of college people, great for families.
Another good idea is somewhere like Cordoba (you have a mega-city and then the mountains and rivers just driving 10 minutes). I use to go to a small town in Cordoba province called Nono, and work in a relaxed environment: a balcony hanging over the river (if I'm lucky to get those rooms), some great wine and great food... you work and disconnect at the same time. However, I'm an urban animal, I can do (and need to do) that for periods no longer than a week and then I feel too relaxed (as in "bored").
Another great option is the beaches, like Mar del Plata and Pinamar, or the Andean cities like Mendoza, Bariloche, Esquel or San Martin de los Andes. Extremely beautiful landscapes, great food, a little expensive, though