For me, I'm wavering between a few items:
Watermelon - Every time I eat a watermelon, I think to myself, "if I had this on a desert island, I'd be the happiest person on earth." It's somewhat nutritious, or hydrating at least, and it's delicious. But it's not very versatile. I can't really use it to make anything else.
Potato - Potatoes are pretty versatile. I could make fries. I could make hash browns. I could mash them. I could use it to thicken broth or soup.
Avocado - It is nutritious, versatile, and pretty delicious. It has a lot of fat, which is probably something I'd be missing in my desert island diet. I could spread it on things, or eat it straight out of the husk. I could make desert island guacamole!
Egg (chicken) - I love eggs. I could hard boil them. I could soft boil them. I could use them as an emulsifier in cooking. I could bake things (kind of)! They are incredibly nutrient dense and I could probably live off them for a long time.
I think I'm choosing eggs. For me, eggs satisfy all 3 considerations: they are nutritious, versatile, and delicious.