Shanghai has a decent enough range of things to buy, but don’t expect things dirt cheap; as far as prices are concerned, Shanghai still can’t compete with Beijing and Hong Kong. However, you can find some nice items in the city’s markets- including clothing (ready made, as well as in the form of cloth, which you can get tailored; Shanghai’s tailors are generally very good) art and antiques. For art and antiques, definitely pay a visit to the Shanghai Antique and Curio Store, run by the government and with a good selection of antiques and souvenirs of different types (what’s good is that at least you can be sure that any antiques you pick up here will almost certainly be actually old, and not just fakes). For art, you could also try the galleries in the area around Maoming Bei Lu.
Two other places, which are worth a visit if you’re interested in shopping, are the Friendship Store at Beijing Lu (it’s got a wide range of clothing, leatherware, antiques and souvenirs), and the night market at Huashan Lu (near Fudan). The night market is set up every evening, and with a bit of perseverance you can find fairly good stuff at low rates.