The first place anyone here will recommend you to go for shopping is KOMTAR. Short for "Kompleks Tun Abdul Razak," it is the largest shopping complex in Penang, a full 65 stories of clothing shops, restaurants, and a couple of large department stores. There's a duty-free shop on the 57th floor. On the third floor is a tourist information center.
Good shopping finds in Penang are batik, pewter products, locally produced curios, paintings, antiques, pottery, and jewelry. If you care to walk around in search of finds, there are a few streets in Georgetown that are the hub of shopping activity. In the city center, the area around Jalan Penang, Lebuhrhaya Campbell, Lebuhraya Kapitan Keling, Lebuhraya Chulia, and Lebuhraya Pantai is near the Sri Mariamman Temple, the Penang Museum, the Kapitan Keling Mosque, and other sites of historic interest. Here you'll find everything from local crafts to souvenirs and fashion, and maybe even a bargain or two. Most of these shops are open from 10am to 10pm daily.
Out at Batu Feringgi, the main road turns into a fun night bazaar every evening just at dark. During the day, there are also some good shops for batik and souvenirs.