I live two blocks straight north of Sherman Circle. The circle has turned into quite the meeting place for families with kids and families with dogs (my wife and I!) The city has recently installed lights from the outside of the circle, pointing in, which illuminate the whole circle. The actual circle is run by the NPS (sigh) and they won’t do anything, so the best we can do is get lights outside pointing in.
There are definitely a lot of young families in the area, and even in the year and a half my wife have lived here, I have seen more and more families. I really love the area. I would definitely say drive around at night and stuff, and see how you feel. I feel quite safe here, however when my wife and I come home late at night, we do take cabs.