Mount Gay is the oldest rum brand in the world, and its visitor centre in the Spring Garden Highway area offers tours that cover the history of Barbadian rum-making and the distillation process, ending with a structured tasting. It is not the actual distillery — production happens at the factory north of Bridgetown — but the centre is well-set-up and the guides are knowledgeable.
The tasting is the point. You work through a flight of Mount Gay expressions from the entry-level Eclipse to the aged XO, and a guide explains the differences in wood, ageing time, and blending. There is a shop selling the full range, including some expressions not available outside Barbados. Tours run several times daily on weekdays; check the website for times. Combined tours with the St. Nicholas Abbey are available if you want to see a working plantation distillery further afield.