The Bridgetown center is around the area of Queen's Park and the area of St. Patrick's Roman Catholic Cathedral.
Below are reviews of the city of Bridgetown, Barbados from an actual visitor's perspective.
Friendly people, great food, and good duty free shopping if that's your thing. It was an old British colony so the architecture reflects it. The series Outer Banks on Netflix staged a car chase there, they had originally said it was Bahamas but I recognized Bridgetown.