If you visit Yogyakarta, then you must visit Borobodur temple (located NW from Yogya) which is one of the most famous temples on Java and the largest buddhist temple in the world. You might also want to visit Prambanan (hindu) and Sewu (second largest buddhist temple on Java, right after Borobodur) which are located just a short drive from Yogyakarta.
Candi Prambanan or Candi Rara Jonggrang is a 9th-century Hindu temple compound in Central Java, Indonesia, dedicated to the Trimurti, the expression of God as the Creator (Brahma), the Preserver (Vishnu) and the Destroyer (Shiva). The temple compound is located approximately 17 kilometres northeast of the city of Yogyakarta on the boundary between Central Java and Yogyakarta provinces.
Sewu is an 8th-century Mahayana Buddhist temple located 800 meters north of Prambanan in Central Java. Candi Sewu is actually the second largest Buddhist Temple complex in Indonesia after Borobudur and predates nearby “Loro Jonggrang” temple at Prambanan. Although the complex consists of 249 temples, the name in Javanese translates to ‘a thousand temples,’ which originated from popular local folklore; The Legend of Loro Jonggrang.