There are only certain areas that are affected by gangs. I don't know where those apartments are located, so I can't say if they're in a bad area or not.
The areas with the best reputations in Greensboro are in area codes 27407, 27408, 27410, 27455 and parts of 27403.
Pleasant Garden, Oak Ridge, Stokesdale, Summerfield, Julian, Climax, Level Cross, Madison, and Mayodan are small communities near Greensboro that also have good reputations. (I've probably forgotten a few.) They're all mostly rural places, but not far from places of interest in Greensboro like shopping and restaurants.
The best schools are in northwest Greensboro - 27408, 27410, 27455.
Like Greensboro, Winston has its good and bad areas. Unfortunately, I'm not very familiar with that area.
I wish you all the best.