Big C has good shops. And the prices are low, and the range is huge. From food, to furniture/appliances. There are imported products, even Russian ones like kefir, cottage cheese, and dumplings. They bake normal bread. There are maximum discounts on finished products in the evenings.
A wonderful shopping mall in a non-resort area of Phuket. You can buy everything here: fruits, souvenirs, household goods, and the services of qualified Thai massage therapists.
Simply the best supermarket in Phuket. In the basement there is one of the most delicious Tom-Yams, for only 100 baht. The supermarket itself has a complete set of everything you need. And it's cheaper than a Lotus.