Jakarta's a good place to shop for traditional Indonesian handicrafts, because some of the best crafts from all over the country find their way to the capital's markets. Keep an eye out for some distinctly Indonesian crafts- batik work, woodcarvings, silverware and jewellery, brassware, porcelain and antiques. An area you make like to visit is Jalan Surabaya, the site of a flea market where you can, with a little bit of luck, make some good bargains (bargaining is almost essential- almost every stall-holder at the flea market starts off with terribly inflated prices). Also keep in mind one more thing- a lot of stuff being passed off as antique may be no older than a month- there are lots of imitations floating around. The government also has an outlet, called Rumah Indonesia (Centre of Home Industry Product), where you can get hold of some good handicrafts. For a completely different kind of shopping experience, make a visit to the Pasar Burung, the Bird Market- an interesting place indeed, where, even if you don't buy anything, you can enjoy the beauty of the birds and their songs.
For more mundane, daily-use items, there are lots of shops as well as supermarkets and shopping complexes where you'll be able to find nearly everything you're likely to need.