If you haven't, please do so, they are a lot of fun to visit and you can really see some of Thailand's 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 the Island on any given day; you just have to do your research to find them.
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 shopping at the markets.
Almost all the local restaurants on the Island pickup their fresh produce each and every 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.