Twenty four hours are all you need. Indonesia is an amazingly colorful and diverse country. The sooner you can get out of the polluted and congested Capital, the better. You can see everything you need to see in Jakarta in 36 hours, but my guess is that after 24 you'll be ready to hop on a bus or train. Or, you could hitch a ride with random people you met the night before to Bandung.
T.K. and Fred visited Jason in Beijing in November 2007. They checked out the Olympic grounds under construction and got WAY more than they bargained for.