Healthy Belize is one of my favourite places for fresh veggies, fruits and now they do seafood too. Their fruit and veggies are organic and quite delicious. Their Facebook page is
Healthy Belize's Facebook page +1
Fruits and veggies are stored in coolers and are marked with the date they are picked. They are sourced from Sol Organic Farms on the mainland so are sustainable and organic. The prices are completely in line with the Green House and other places that sell non-organic items. Try them!