In my opinion, you can travel to pretty much anywhere, depending on your appetite for risk and willingness to implement security measures to ensure your safety. With regards to Rio De Janeiro, I think it’s safe to attend the Olympics. The chances of being a victim of a terrorist incident are slim, but the chances of being a victim of a kidnap, robbery or violent crime are more likely.
The level of street crime is dangerously high and although there will be a massive police and/or military presence in and around the Olympic venues, other areas of the City will not have coverage. There have been several reports of athletes being victims of express kidnaps and robberies pre-Olympics, and this will probably increase during the Games.
While everyone is focused on crime and terrorism, I think the risk of political unrest, getting caught up in some kind of violent protest action is high. Travelers could unwittingly be cut off from their hotels or groups and then be vulnerable to injury or arrest etc. The probability of a vehicle accident and/or medical mishap occurring is very high. The availability of quality medical care and emergency response services will certainly be tested throughout the Olympics.
Have a plan. Ensure your plan extends beyond the sights and sounds of the Olympic experience. Situational awareness is key. Be aware of your surroundings. Know the contact numbers for your Embassy or Consulate. Make sure your mobile device works overseas and you know how to use it locally in Brazil. Identify medical facilities ahead of time and make sure your insurance will cover you if needed. If your existing insurance will not cover you, purchase protections that will. Keep abreast of changing threat dynamics through available media outlets – newspapers, television, social media, etc. Secure transportation ahead of time and avoid public transportation as much as possible. Know what to do and where to go if a crisis event occurs during your Olympic experience. Speak with hotel staff or Brazilian friends about what is going on. Stay away from the area of official Government buildings that might be the focus of a protest or terrorist incident. Make sure you can get in contact with your fellow travelers, groups in case you get separated.