There's no doubt the Central Market would top this list, even if your not buying anything it's great for a saunter round although it would be difficult to leave without purchasing at least something.
The Farmers Market at the Adelaide Showground on a Sunday morning is also very good with a fantastic selection of good local produce.
For clothes and craft etc, Gilles Street Market every other Sunday is a good choice with plenty stalls and a nice atmosphere with a live band or DJ.
Adelaide Central Market is an institution. They have some fun things happening this July 2014 school holidays http://www.weekendnotes.com/adelaide-central-market-july-school-holiday-fun-2014/ For fantastic weekend veggie, produce and some new goods plus trash and treasure look no further than the Gepps Cross Sunday Market. Also an institution in its own right. A fantastic experience. http://www.weekendnotes.com/gepps-cross-sunday-treasure-and-food-market/
If you want fresh fruit, vegetables and produce directly from the farmers I recommend Farmers’ markets, 25 minutes from the city along the freeway at Mount Barker. All the food is seasonal, you’ll enjoy the village ambience of one of the Adelaide Hills.