In short
Yogyakarta is the only sultanate still recognised in Indonesia, with its own administrative status. The kraton, the sultan's palace, is still lived in and can be visited.
Borobudur, the largest Buddhist temple in the world, and Prambanan, Java's great Hindu complex, are less than an hour away. Both are World Heritage sites.
What it really costs
This is one of the cheapest cities in Indonesia, far below Bali. Its student population keeps cheap housing and eating options alive.
Warungs serve a full meal for one to two euros. The food budget is the lowest anywhere in this Asian catalogue.
What nobody tells you
Climbing onto the structure of Borobudur is a separate ticket from entry to the grounds, capped in number and at a fixed time. It is booked on the official site before you come.
Merapi, thirty kilometres away, is one of the most active volcanoes in the world. Sunrise excursions depend on its alert level and are cancelled without discussion.
The rainy season, November to March, drowns the sunrises over Borobudur — the main reason for many visits.