I can't think of anything really worth seeing in Jakarta, we lived there three years and always went out of town for sight-seeing.

Point to point not long distances but traffic is a mess and can take literally hours. Food is great, lots of music spots and shopping for 'antiques' is fun.

A one [or overnight] day trip to Borobodur in Yogyakarta is definitely worth the effort. Strongly recommend setting up an English speaking guide, it's not prohibitively expensive [at least back in early '90s].