I've only bought a desk and bed in China, so take my advice with a grain of salt...

There are some really high-end furniture malls. There are also super cheap furniture back-alleys. I think IKEA fits in the middle pretty nicely. I don't know what you mean by small pieces, but if it's just an end table and you don't care much about looks, then you can get a decent collapsable wooden table from a local vendor for ~40 kuai (that's Chengdu price, don't know about Shanghai).