If you're a foodie, and love to cook, by all means stay at a place with a kitchen, even if you don't cook when you are there, you'll have a frig to keep Belikins, etc. I've done it both ways. The first time I didn't cook. I was not sure about the grocery stores, etc. and traveled with a friend who had been there many times, but she is allergic to cooking
and could not provide me with any info in that area.
The second time I came prepared with a few things in my bag that I knew would be pricey and they were easy to pack. I found a little produce shop that had everything fresh that I needed and a couple of larger markets located across from each other that had everything else. The meat is frozen, but everything we bought was great. Milk, eggs, bread were very fresh.
We went fishing and I enjoyed cooking the fish that we caught. Some of it I used to make our Christmas Dinner.
Capt Jeff is correct about the full day of snorkel/fishing/bbq on the beach - we had an awesome time and there is nothing like fresh catch, cooked for you.
The lobster is not like Maine lobster. They are smaller and if they are over cooked become like rubber (experienced that in a couple of restaurants and would have done a better job myself.
Next time I go, I will cook, because when you are a foodie the cooking becomes part of the adventure.
Enjoy your trip!