In Jakarta you will find a broad variety of museums. In the north of Jakarta, Jakarta Kota, are the most museums situated. This area is an old Dutch area which you can still see in the buildings and the typical old Dutch bikes that are for rent in this area. The old building of the governor from the Dutch VOC is now serving as an history museum of Jakarta.
In this same area you have a Wayang museum. This museum is situated in an old Dutch building and is all about the Javanese Wayang Puppets, and they also have some international puppets. Inside there are even some old Dutch graves from the 17th century.
Also in the North of Jakarta is the National Indonesian museum. Here you will find all the interesting facts, from clothing until buildings, from many of the Indonesian islands. The entrance ticket of the National Indonesian museum costs 10.000 RP. It is quite big and you can spend a few hours walking around here.
Taman mini is similar to the National Indonesian museum, describing the culture of the Indonesian islands. But Taman mini does this in real-life scale. The houses from all around Indonesia are rebuild in this area and you can make a small walk like if you were in Bali and another hour later you will find yourself walking through Sumatera. This park is also too big to see all in one day, but you can take a cable way over the park to get an impression of how big it is. Also during the cable way you have a good view over the lake they build in the middle of the park, which contains the islands of Indonesia, giving you an impression like you are flying high above Indonesia to see it all at once. The entrance ticket to the Taman mini park is just 10.000 RP but the cable way costs 30.000 RP.