The Six Degrees backpackers hostel in Jalan Cikini Raya. It's fairly new and has become quite popular recently. Apart from the dormitories, they have single, double and twin rooms.
Take the DAMRI airport bus to Gambir (30,000) and a Blue Bird taxi to the hostel ( (15,000; you can also walk). Jalan Cikini Raya is a pleasant area in Central Jakarta.