Yogyakarta is the one city on Java where the old court culture is still lived rather than displayed. The Kraton remains a working palace, its retainers still walking barefoot across the pavilions, and the streets around it still make batik the slow way — wax, dye, wax again.
Most travellers come for Borobudur and Prambanan, and they should. But the city rewards the days on either side: the silversmiths of Kotagede, the Friday night gamelan, the food carts on Malioboro that only appear after dark.
It is also the easiest place on Java to slow down. Distances are short, the coffee is good, and nobody is in a hurry.