I spent a week there in September 2008 - had a great time, but I went on my own and I'd love to go back with someone (this isn't a request to join you, lol)
A helicopter tour over the island, taking off from Bridgtown is pretty neat and was relatively cheap (I think it was $90 for an hour and a half):
I assume it's still a thing, but every Tuesday and Friday they hold a big communal fish fry in the Oistins part of the island (south coast) and that was a good laugh
The Andromedia Botanic Gardens in Bathsheba were pretty cool if you like that kind of thing. Weirdly I can't find my photos of these two things though, which is annoying as I took some great photos of the flora!
Truth be told, I didn't actually *do* an awful lot while I was there. I rented a little Mini Moke for the week and spent a lot of time driving around the island which was vaguely terrifying without satnav on my phone, probably a bit easier these days:
All the beaches are public (even the ones in the super posh areas) so feel free to rock up to any of them - but bear in mind that any furniture (sun loungers etc.) may not be for public use!