Worthing was my base when I stayed in Barbados. It is located about 4km from Bridgetown in the south-west of the island, and is based around a strip of shops and restaurants on Highway 7, which connects the capital with Grantley Adams Airport. I guess you could call it an outer suburb or Bridgetown. It's close enough if you need to go to the city for anything and far enough away to maintain a quiet atmosphere.
I stayed in Worthing for a week and got to know the neighbourhood fairly well. Everything is more or less based on the one street. It's a laid-back and friendly area and I always felt safe there, day and night.