If you like to hike as well as bike - or perhaps these trails are also bikeable:
http://www.puncaktrek.com/ has maps of a circuit around Puncak
Java Lava is a popular group of expats and Indonesians that hike peaks in and around Indonesia. They have a website now with more information about the group and its activities:
I think this is another offshoot from Java Lava but it has specific ratings and descriptions of all the peaks above 1000m in Indonesia (or interesting peaks under 1000m).
A new group that does hikes and adventure racing.
I'll add more hiking sites as I come across them.