In general anywhere closer to the outside of the city is better - North Worcester around Burncoat street, East side around Lake Ave or the west side around Worcester state/Salisbury street west of park Ave. I’ve lived in less desirable parts of the city since 2009 and I’ve never had any issues except a few instances of very minor car vandalism, neighbors getting arrested and the occasional parking dispute in the winter. Its definitely not as bad as the worst parts of any major city. I’m single, live alone and mostly keep to myself so things don’t bother me much.