It depends on what you are looking for. Brazil is Brazil, warts and all (and there are plenty of them) and all of it contributes to what makes Brazil unique. However, many tourists feel more comfortable in a neighborhood that most resembles what they are used to at home, both physically and demographically, which in Zona Sul is probably Leblon and Ipanema. Many Brazilians with the income to do so aspire to live in neighborhoods where their money can buy them what they hope will be a more tranquil daily life at a distance from the more problematical facets of life in Brazil. In Rio, with the poor neighborhoods literally right on top of the wealthier ones in the Zona Sul, that can be harder to do. There is sometimes bitterness expressed about that.

IMO Copacabana is great for people watching and has a very lively main shopping street, and a mix of restaurants. I have friends who grew up there in big, old, airy apartments, and friends with studios overlooking the beach, from whose perspectives I have enjoyed the neighborhood. I also have friends from the hillsides with whom I have enjoyed the beach.

Insofar as "warning" or "scaring" newbies, there is a very fine line.

(And yes josephstern, iPhones are still a "draw". They are expensive in Brazil, more so than other brands. Brazilian "ingenuity" makes them useful again if stolen.
Disclaimer: I am more into utilitarian than trendy. My personal iPhone is worth about 35 bucks on the used market in the US, a model old. However at the current exchange rate, that represents about one fifth of a monthly minimum wage used to support a family in Brazil.)
Too bad all the 'ingenuity' and energy that goes into crime in Brazil, from politicians to pivetes, can't be channelled into other areas that might better Brazil.