Ipanema is the Safest (and most expensive) Area in Rio de Janeiro

You'll pay a premium for being in this area, but you'll be much more at ease here. With copacabana (which I discuss below), there is a higher rate of snatch and grab robberies/thefts which occur on the street. I've seen a number of them: they are usually teenage boys who are solo or in a small group who run up to an older person or woman and grab their celular phone and run off. It is important to note that this can happen in Ipanema as well. 

The buildings in Ipanema are more well-maintained and have slightly better security. The people who live in the same building as you will be slightly wealthier, and themselves more willing to invest in things like cameras on each floor etc..  Theft is a concern in all parts of Brazil. It is how the locals in each area handle that it that is key. 

Copacabana is a Safe Bet for Safe Long-term Renting in Rio de Janeiro

There are more options and availability in Copacabana. It is still one of the safest parts of Rio to live in as a foreigner. It is larger and slightly cheaper than Ipanema.  What makes the area safer than the north of Rio (which is the poorer, more dangerous area of Rio de Janeiro), is that its infrastructure is more developed and the police presence is significant.

Protecting the tourist trade is important to the Brazilian economy, and the local Rio de Janeiro government makes special provision for police task forces in the tourist regions of the city, ie Copabana and Ipanema. The fact is there are a substantial number of police officers at various checkpoints in Copacabana and they take their job seriously. Many expats and digital nomads end up in Copacabana for at least some part of their stay in Brazil.

Barra da Tijuca is a Safe Suburb of Rio de Janeiro

Were it not for the fact that finding an Airbnb to rent long-term is slightly more difficult in Barra da Tijuca (or just the word Barra as it is referred to locally), I'd recommend this neighborhood as the best overall choice for expat and digital nomad living in Rio.

It is quite safe here, though not to the degree that Ipanema is. You will find that it really has the sort of feel that suburbs in the United States have: spread out (more room), larger residences, wider roads, and plenty of well-stocked shopping malls (the best shopping mall in Rio as a matter of fact: Barra Shopping). I appreciate the fact that everybody is not living on top of one another the way they are in Copacabana. Barra is less crowded than Ipanema and Copacabana. I have a separate video where I discuss Renting and living in Barra da Tijuca.