Are there any shops selling these near there, or do I have to find a real market?
Well there is Jason’s supermarket in the basement of QSquare, the bus station next to Main Station. And Tianhou, the organic supermarket is a couple of blocks away. Even Mitsukoshi, across from Mai Station, has a supermarket.
There are several small fruit shops on BoAi Road, but those are high end.
Closest traditional market is Chengzhong, on Wuchang road.
EDIT:
Forgot about Zhongshan Market, on Chang An road and Zhongshan intersection. It has plenty of fresh veggies and meats.