Enjoy your trip, I was not into figs when I visited so I'm of no help. there are some gardens you can visit. The Island is small but beautiful and if it does have figs this should be a great time to visit. The people there seemed to be very friendly also. I hope you report on your findings
A few pics for you
Light house

Natural Bridge

At Bridge quench your thirst

I was there a couple years ago. I have to say, I didn't see one single fig tree there. It's very dry, and nothing but cactus trees thrive there. Around the resorts you'll find many mango trees, bananas, and coconuts. I visited an Aruban friend down south near baby pool and he has a garden of all fruit trees, however I didn't see a fig. So don't keep your hopes up for local varieties there. I'm sure someone there has a fig tree, but they probably brought it from somewhere else.
Lots of tasty iguanas.

Bass