Jakarta is a mall city. Shopping centers are where Jakartans socialize, eat, and escape the heat, and the range is vast. Plaza Senayan and Senayan City in the south are upscale; Grand Indonesia and Plaza Indonesia on Jalan Thamrin are the glitzy flagships; Kelapa Gading Mall in the north is one of the largest complexes in the city.
For something more local, the markets are worth exploring. Pasar Baru for textiles, Jalan Surabaya for antiques (or convincing fakes -- bargain hard), and the various street markets around Glodok in Chinatown for everything from electronics to dried goods.