Have you ever been to a Phuket open market? If you havent, please do so, they are a lot of fun to visit and you can really see some of Thailands most famous foods. Yeah, you can just go to the local grocery store and get just about everything you need, but nothing beats an open market experience.
Open markets are located all over Phuket on any given day; you just have to do your research. Once you get to the market it is very easy to get overwhelmed, but think of it as saving a bunch of cash and really getting some fresh food, you could literally saves hundreds of Baht by using the market. Almost all Phuket restaurants pickup their fresh produce each day.
So my advice to you is, when you are in Phuket, find an open market and enjoy all the wonderful foods from Thailand, it really is a joy.