There is one market in Phuket that was once called 'Talaad Thai-Rot' (roughly translates as 'Car Boot Sale') and it proved to be enormously popular but the cars soon took up too much room! Still, the market proved so popular that it was swiftly converted into a standard affair (with no cars) - but only at the weekends. Most of the stalls open about 16:00 and they start to close at 22:00.
Take the road south from Central Festival leading towards Wat Chalong and you'll find the the market is opposite Wat Naka - you'll see plenty of people and cars so you'll know when you've arrived!
The market is a myriad of scents, people of all ages, noise and goods for sale.
There are a plethora of traditional Thai market restaurants and some are not for the fainthearted - I still find 'insects' a difficult dish - I dare you to have a go.
Remember that it is not a market specifically aimed at tourists, but that's exactly what makes it so fascinating for visitors - this is a slice of the 'real' Thailand.