Just south of Bridgetown, there is some pleasant, flat coastal running between Rockley Beach and the Needhams Point lighthouse. It’s about 5 km (3 miles) out and back. The ~2 km between Accra Beach and the Camelot House in Hastings is known as the South Coast Boardwalk, which has some great beach and water views. Heading north, the sun will be at your back in the morning. For sunset views, head south (from Camelot).
For a nice add-on, do a loop around the Garrison Savannah using Garrison Rd., a historic horse racing track with a unique grass oval. This adds about 1 mile to the route. At the northern end of the oval is the Barbados Museum & Historical Society.