Expo Phuket or Expo Market, is a huge indoor clothes and accessories market in Phuket Town. The Expo Shopping Market is Open daily during normal hours, and here you can find just about anything related to the current fashion, even if mostly catering towards teen and children, it's a great place to start your shopping spree, keep in mind that the target group for this market is bargain hunters, without a particular brand in mind. Teen Girls will simply love the place, and since the prices here are very good compared to what you would pay elsewhere, you should consider visiting this while in Phuket Town.
You won't find only clothes here, there is some other handicrafts and fun stuff to browse, so be sure the teen boys will have their fun also. Clothes and goods are usually "imported" via Bangkok directly, so that's how they keep the prices down, and the constant flow of new fresh looks and things.
If you are in Phuket for a long time you might consider a visit every couple of weeks, to see what's new. Also if you happen to miss the weekend market, and are looking for something similar this is a good place to visit.