Bamako's Grand Marché is the city's commercial heart and the best place for anything from fabric to fresh produce. Look specifically for bogolan (mudcloth) — the hand-dyed cotton cloth made using fermented mud is Mali's most distinctive craft, and you'll find it here in a wide range of quality and price.
The artisan market near the National Museum sells woodcarvings, bronze figures, jewellery, and leather goods at prices that allow for serious negotiation. There's a wide range of quality; take time to look through properly before buying. Tuareg silverwork from the north (available here even when travel to the north is inadvisable) is worth seeking out.
For everyday goods, the neighbourhood markets around Médina and Bozola are more authentic and less expensive than anything near the tourist hotels. If you're looking for Malian music recordings, ask around the music venues — bootleg CDs and the occasional legitimate release of kora and balafon music circulate in the same informal economy.