Harrison Cave is a nice and well run cave, but it is small in comparison to some of the caves you'll find in the US. If you've seen other caves, this won't add much to your "cave experience". However there are some other nice attractions close to the Cave, e.g. Welcchman's Gully. Another data point is that the Cave gets very crowded in the heart of tourist season, with waits to enter via tram as long as 2hrs, but I've heard the average is more like 1 hour.
I love to snorkel, so my choice would be to go snorkeling. I've not found a really good location on Barbados to snorkel. Where are you considering going? Folkestone Underwater Park?