There are nice neighborhoods near Watts. Duke Park, Watts-Hillandale, Old west Durham, Old North Durham, Northgate Park. Do a search for Apple Realty or Bob Schmitz properties. Durham's a nice city to live in & raise kids. Don't fall for the hype about crime--there are crappy neighborhoods and their are decent neighborhoods, and the cost of living is best in Durham out of the 3 cities in the Triangle.
PM me if you'd like more info. I heart Durham.
@porterwoman, Im lookin got relocate to Durham, for school. Would you say that the neighborhoods you named are still considered to be good? I have been looking for apartments and really have no clue about Durham. What would be a nice neighborhood, to raise two little girls???