So first of all get a SIM card to get internet there if you are planning on staying more then 2weeks in Indonesia. It's worth it. Second instal the app "Grab" best way and more fair way to go around Jakarta.
Go there it's 40.000 for 2 persons. Then you kind have 3 choices. Go by foot (at least 4 to 6hours walking) go by bicycle/motobicycle (takes 3 to 5hours) you take time to see each part of Indonesia what you loose time it's going to each zone. The third it's going by cable car (80.000 IDR I think) Then you are high and you can see a lot in 20 min and chose.
By the way be careful you are not in Ramadan half of it it's closed.
The reptile museum it's ok to go ;) More