Even though its highly rated on Tripadvisor and locals will tell you to go, skip Harrison's Cave! It is boring and not worth the time or energy to get there.
Renting a car is easy but driving around the island is not. Traffic and roundabouts can be confusing. If you want to explore the island, efficiently, I recommend hiring a driver to take you.
The food in Barbados is pretty disappointing; overpriced and mediocre. The best meal I had was at Apsara Sumdra, an Indian/Thai restaurant that has a lovely ocean front patio. Besides eating at Apsara, I sustained myself on fresh coconut and avocados from local street vendors.