Although not known as being one of the most dangerous neighborhoods, you are still in the city, and you should be on your look out.
For example, in the last week there have been 9 assaults reported in the Russina Hill neighborhood (excluding the Columbus and Broadway where the strip bars bring with them rowdy behavior).
Since the beginning of the year there has been only one murder in the area (at the corner of Columbus and Broadway).
In other words, I would not go out for a late night stroll by myself and that sort thing. If you use common sense though, you should be okay.
