For most shopping in Gozo (other than local crafts and village store stuff) Victoria is the place. Here you will find a street market in and around the main square (Independence Square or It-Tokk), supermarkets and a good department store as well as plenty of independent shops. We even managed to get replacement prescription glasses for my son in a matter of a couple of hours.
For local crafts head to the Ta’ Dbiegi Craft Village between the San Lawrenz and Gharb. This complex of small buildings houses crafts workshops and shops. You can watch Gozo glass being blown and silver filigree being made. Craftwork in metals, onyx, leather, wood, glass, wool and lace is on sale. It's a good place to buy souvenirs large and small. The complex is open 10am-5pm daily but each studio/shop keeps its own hours and fewer are open in winter.
For general advice on shopping in Malta, see my Shopping in Malta page.