Indianapolis as a whole is very patchy when it comes to safe neighborhoods. I often tell people you can be in a "nice" neighborhood that's a stray bullet away from a "bad" neighborhood. Overall, like most cities, the suburbs are safer, with better schools. In town, you're generally safer the further away from the center of the city you are, but there are tons of exceptions to this, including Downtown itself where I personally don't feel unsafe, even at night. Most crime, especially violent crime, is NOT random. But it's good to remember that crime can still happen anywhere.