Rio is a hit or miss, one never knows. I've been there many times and never had a problem, but it's important to be careful and avoid situations that can become dangerous: public transportation, walking dark streets at night, or even being alone in an area you're not familiar with.
I would stick to the Zona Sul area (south zone) of Leme, Copacabana, Ipanema, Leblon and Barra da Tijuca. But even in these areas, considered safer, try to avoid carrying too much money, expensive cameras, watches, etc. The idea is to blend with the rest of the people. Always ask locals you know and trust (hopefully you'll have some) or people in your hotel where it's safe to go and what to avoid. They know.
With all that said, Rio is a magic city, full of energy, music and dance, and despite all the problems a place I love to go back to.
Hope it helps.