• Sono Budoyo Meseum.
  Here you can find javanese art likes puppets, kris (traditional     dagger) and batiks. And this museum is the second biggest at Indonesia.

• Royal Horse Cart Museum.
  Its holds 18 centuries old chariouts of the sultan.

• Hamengku Buwono IX
  Its display private possesion of the sultans and set of replicas of royal paraphernalia.

• Fort Vrederburg
  This is an old dutch fort built infront of Yogyakarta Kraton Place, nowadays is being place to organize art and exhibitions.

• Ulen Sentalu
  You got to see this, although take by 1 hour drive to Ullen Sentalu (Kaliurang) i thinks is worthed to see. Here you can find collection the entire range of royal dresses of the palace from the edge and present.

• Museum Sasana Wiratama
  This museum was build for Price Diponegoro for his bravery against Ducth Colonials. At this museum you can find collections of Princes Diponegoro belongings.
• Jendral Sudirman Museum
  Formerly this is was a residence of Panglima Besar Jendral Sudirman, he has the first general of Indonesian Army.

• Affandi Museum
  It was house and studio of Affandi, he was international painter. This Museum has uniqe design and located at side of gajah wong river.

• Museum DIrgantara
  I thinks this museum has uniqe site, here you can find old forces of Indonesia, Such Bommber, Fighter, helicopter, Scud Rudal, Radar, Tank, and other Forces.

Thats it, if i find more museum, i will posted again.