We have a small grocery store and gourmet store on the island and two large grocery stores over in Port Isabel. If you can't find what you want nearby, Brownsville also has a large selection of establishments.
Blue Marlin Supermarket
This is our little grocery store on the island. If you don't plan to do a bunch of cooking, this is the place to go.
They have great meat and specials all the time. The bakery is pretty good as well.
2912 Padre Blvd. at Dolphin, South Padre Island
The best cajun seafood and fried seafood on the island!
Fresh seafood to buy as well.