Phuket Square is the major part of Jungceylon Shopping Mall, and it hosts Robinson Department Store that occupiers most of the shopping centre, Powerbuy for all sorts of electronics, Big C Extra supermarket, B2S that sells books, SF Cinema City. Here you can enjoy a movie, or have some of you family enjoying one while you enjoy the shopping.
On the third flow you have IT Island, with smaller stalls that sell all kinds of IT related stuff. banana IT a well known electronics chain in Thailand, Magic Theater for magical stuff, Mega force, SF Strike Bowl, SF Cinema City and XD Theater.
Besides all this Millennium Resort Patong is also located within the shopping complex. The whole shopping complex is well worth a visit, even if shopping is not your thing, there is plenty of other stuff to do here, and it is a good place to get a bit of distance from the beach life on a rainy day, or a too sunny one.
And when you had enough of Jungceylon shopping mall, there is always Central Festival shopping mall in Phuket Town, or Home Pro Village in Chalong. And don't forget Tesco Lotus shopping Mall, and BIG-C shopping mall just outside Phuket Town near Central Festival.