The best place to buy produce is off the back of a truck, but they will only carry a dozen items or so.
Eggplant, yucca, plantain and bananas, potatoes, pineapples, oranges, limes, coconut onions and cucumbers are the foundation of Dominican produce-- anything after that you will prob have to go to a bigger store.
There are some very good peppers in the DR. The pencil thin ones are super hot and the yellow and orange ones that look like habaneros are actually sweet. Basil is very cheap. The plum tomatoes are better than what you find in the US. The potatoes in the DR are similar to Yukon Gold in the US and are excellent.
My favorite meal at home was Bavette pasta with pesto, garlic and fresh diced tomatoes. Playero carries Barilla brand Bavette. It has a half moon cross section. Puree some basil leaves with some garlic in a blender with some olive oil. Cook the pasta and set aside to drain. Heat the pesto with a splash of white wine and toss the pasta in it. Take off the heat and add in some diced tomatoes, and serve with some grated Parmesan cheese on top. The pesto keeps for a week or so in the fridge or much longer in the freezer. I think you can also get fresh wet mozzarella in some stores so you can also make a caprese salad.
I shopped at about six to eight different stores in a month. There is no one best store for everything.