Image © Mike Aquino, licensed to About.com
If ever there were any doubt that Yogyakarta ("Jogja" to its residents) was the center for Javanese high culture, the Yogyakarta Kraton ought to put them to rest: the palace serves as the home for the Sultan of Yogyakarta (who has managed to preserve his line's prerogative to rule), a center for Javanese performing arts, the focal point for Yogyakarta's religious and cultural festivities, and a landmark for the whole city, for which the Kraton is the hub and beating heart.
Yogyakarta is located in central Java, just an overnight train ride away from Jakarta; to plan a Yogyakarta itinerary of your own, read our list of top things to do in Yogyakarta. You should also read up on the museums and tourist attractions around the Kraton.