Two questions on Bermuda
The farmers market in Hamilton is only open on Saturday as are the vegetable stands in Smith's on South and Middle Roads, usually from 8 a.m. to noon. You can, however, find local produce at most supermarkets - try Lindo's in either Devonshire or Warwick, the former may be closer to you. Tom Wadson's locally-raised chickens are available there and at Miles Market and the Supermart in Hamilton. Here is the link to Tom's Facebook page:https://www.facebook.com/pages/Wadson...
Along with vegetables and chickens, he has sausages and lamb, etc. that he raises here. It's also lobster season now, which are also sold along the roadside, if you don't mind live lobster waving those feelers around :-)
Saturday mornings, there is the farmer's market at Bull's Head carpark, in the city of Hamilton from 8am to 12 noon.
You might also drive past random stalls at the side of the road, vendors selling fish or veggies, I'm not sure of times they're open or when they show up. The only one I don't like is the gentleman selling fish on Trimingham Hill road, my problem is when I can smell the fish from the bottom of the hill, I'm guessing it isn't that fresh.
Windy Banks farm also has a stand on their premises, they're located in Smiths Parish. They have a mix of cooked foods and veggies. Wadson's farm also has a stand open Mon to Sat, they're located in Southampton Parish, veggies and meats. Both have Facebook pages where you can get more info.