The rupiah (IDR) is the official currency of Indonesia. There are plenty of exchange facilities all over Yogyakarta main tourist areas, most of them accepting currencies like the US dollar, Euro, Australian dollar, Ringgit MAlaysia, Singapore Dollar, and UK pound. 

You can have your money changed at the following locations :

#1. Banks 
You are least likely to be ripped off when exchanging currency at a bank. Alternatively, you can withdraw from a bank ATM using your debit or credit card.
Most banks in Yogyakarta accept foreign currencies for exchange. On weekdays, banks in Yogyakarta are open from 8am to 3pm.
Big names such as BCA, Bank Mandiri, BNI, CIMB Niaga, etc usually offer money exchange service.

#2. Hotels
Many hotel front desks permit currency exchange, but offer lower exchange rates compared to banks and regular money changers.

#3. Authorized money changers
Bank Indonesia-authorized money changers advertise their status as Pedagang Valuta Asing Berizin or PVA Berizin (Indonesian for "Authorized Money Changer"). 
There are 2 reputable money changer in Inna Garuda hotel on Jalan Malioboro near the train station. Barumun Abadi and Mulia Money Changer. 
Mulia have branch in Ambarrukmo Plaza (near airport) opens until  7 - 8 PM.

Note : Keep always wise to count your money at the desk before leaving just to be sure in your own mind that all is well.

Otherwise, There are lots of places that you able to use your Credit Card. 
Visa & Mastercard is widely accepted as method of payment in most big restaurants, hotels, and big shopping centers. Lots of ATMs also accept Visa & Mastercard


Source : summary from Intternet review