Yogyakarta is in Java, and is believed by many to be the perfect embodiment of Java and all that is Javanese. It's in Yogyakarta that the culture of Java has been best and most completely preserved. PrambananTemple, Yogyakarta
Yogykarta was at one time the capital of the Mataram kingdom, and remained an important city even in later times- the Sultan's Palace was built here in 1755, and even today is the core of the city's traditional and cultural life. It's a huge building, and actually holds within its walls, two museums, various schools, mosques, offices, markets, and silver and batik workshops. In addition, occasional performances of traditional dance and `gamelan' orchestras are held here, so it's the perfect place to come for a good dose of Javanese culture.
But Yogyakarta isn't just the Sultan's palace; there are other sights to explore too. Chief among these are the magnificent Prambanan Temple (locally called the `Temple of the Slender Virgin'- a Hindu temple which is widely regarded as the largest and most beautiful in the country) and the Taman Sari (the Water Palace), a 1700s pleasure park, though rather dilapidated now, still shows signs of its past splendour.
Also of interest to many visitors would be the Museum Sonobudoyo, with its display of Javanese artefacts (virtually everything from musical instruments and antiques to `wayang' puppets representing long-nosed Dutch soldiers!). In fact, if you'd like to buy some wayang puppets or other local handicrafts, Yogyakarta is a good place to spend your money- you'll probably be able to get some good stuff at rates much lower than what you'll find in the larger and more `touristy' places like Jakarta and Bali.