The best place to learn about traditional local weavings is the Museo de Arte Indígena, but to buy them you are best off going direct to the villages. Prices are steep by Bolivian standards, but the items are high quality. Several shops near the central plaza sell locally made clothing, from high-quality alpaca sweaters to cheap ponchos.
A trip to the Mercado Americano, around the junction of Mujía and Reyes, will keep clothes lovers busy for hours, while the enormous and maze-like Mercado Campesino is a fascinating mix of stalls selling traditional and authentic food and everyday housewares and junk. Take micro 7 or G northbound from the center.