Punta Arenas is home to a duty-free shopping center called the Zona Franca, with several blocks of shops hawking supposedly cheaper electronics, home appliances, imported foodstuffs, sporting goods, perfumes, clothing, toys, booze, and cigarettes. It's a massive shopping mall, with big-box stores a la North America. The savings here are very negligible, except for on alcohol, although there certainly is a lot on offer, including a few supermarkets. This does make it a fair place to stock up on supplies if you're planning a backpacking trip to Torres del Paine -- otherwise, forget it. The Zona Franca is on Avenida Manuel Bulnes on the northern outskirts. It's open Monday through Saturday from 10am to 12:30pm and 3 to 8pm, and closed on holidays.
For regional crafts in town, try Chile Típico, Carrera Pinto 1015 (tel. 61/225827), which has knitwear, carved-wood items, lapis lazuli, and more. For high-end, artsy-craftsy household items, such as picture frames, candles, throws, curtains, and the like, try Almacén Antaño, Colón 100 (tel. 61/227283). Most afternoons see a collection of local artisans selling handicrafts in the city's main square, the Plaza de Armas. Look for wool sweaters and wooden toys there.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.