Are you staying in a one bedroom or a studio? DH and I ate very well on very little money, but had a one bedroom for 7 of the 10 days we were there. All breakfasts were in the room. We bought lunch meats and stuff from Target. Nice produce from the produce store in the same parking lot as Target. Steam Fresh veggies, baked potatoes for the microwave. they have very nice gas grills at the resort, and we also purchased hamburger patties and some steaks. The taco place across the street gives you a lot of food (we had enough left over for lunch the next day). I do NOT recommend eating at the Chinese food place across the street. The Island Market across the street has a nice deli dept. that does made to order salads and has some ready made food too, like fried chicken. I found them pretty reasonable. We did not do any fancy sit down places this last trip.
We were more into packing a lunch into our backpacks and heading out for a day of exploring (we did one day exploring, alternating with one day at resort)
Also, the front desk used to give you a map with local food places. We would also ask some of the local cast members where they like to go to eat.
I just checked the photo I took of the Giovanni's shrimp truck on the north shore, and in Jan. 2014 the garlic shrimp plate was $13.