Your best fruit might just be the starchy plantain. It is actually more similar to a potato than most other fruits and is traditionally cooked like a potato (fried, boiled, mashed ect.) due to it's high starch levels. You can eat it raw, but it doesn't have that overwhelming sweetness like most fruits, and so, is typically served up cooked and seasoned.
Tapioca flour I would do my best to skip. Don't obsess over it as this is your vacation, but don't go trying to add it in to anything. I am generally skeptical of most "flours" anyway.
Rice is generally gluten free. Some people have issues if it is processed in the same factory where wheat has been, leading to contamination though. Rice is an "ok" grain (especially in the white form). Most people don't have issues other than the carb content being pretty high. Just don't go eating bucketfuls of it.
Beans are fine and gluten free as well. But if you've been prone to bowel/intestinal issues lately, their high fiber levels are probably something to be avoided. If not, you should be alright.