The carriage museum is housed in a building to the west of the main Kraton palace in Yogyakarta. The displays of the museum should be no surprise: royal carriages used by the sultans from years past. Some of the special carriages were used in coronation ceremonies while others were for day-to-day use. There is even one that was used for funerals.
The exhibits are a bit dusty - apparently the carriages are only ritually washed once a year, and there are no signs in English, so you need to have a keen interest in such things to visit.
Admission to the Carriage Museum is 5,000 Rupiah (0.30 USD).