Cardón
Due to the Major's policy in the village, you'll find virtually no indigenous arts and crafts. Whatever you see at the handicrafts' markets, you'll find much cheaper in Peru or Bolivia, even Ecuador! The few really local pieces, namely those of cactus-wood, are actually a crime against nature. The wood comes from a severely endangered species of cactus, the Cardón Echinopsis atacamensis, which has been subject to extreme predation by locals. While a novelty, and sure to bring curious glances from everyone, it's not worth it-in all likelihood, whatever piece you bring back home will be detained at your customs. Be a conscious tourist, and avoid that trap!
really
If you want something really local, visit the museum's store. Even if you don't actually want to visit the exhibit, or have already done so days ago, the people at the entrance will let you go in there freely. They carry plenty of books and woven pieces, plus a few curious souvenirs, that were actually made by the community. Some of the books they have are virtually impossible to acquire anywhere else!
Be careful with the peddlers of archaeological findings! There's a few of them. You can be assured that whatever they're selling is the real deal; you can also be assured that whatever you buy will get you in jail. Chilean law punishes the "theft" of archaeological pieces with hefty fines and a stay behind bars. Do yourself a favor, and avoid them. And, if you're still unconvinced, ask a few locals about the curses that befall those who desecrate burial sites...