Right now, hotspots are being placed in some malls in Jogja. As far as i know, in Plaza Ambarukmo and Galeria, there's a free Internet access which can be used freely. In Plaza Ambarukmo, you can access it in the Food Court, while in Galeria, you can access it anywhere, since it's placed on the ceiling on each floor. It's provided by XL or Indosat as far as i can see, since there's a logo for their company.
So, when you visit Jogja, please bring your laptop and give it a try, but perhaps the connection is not as fast as usual for few days, since i think the Internet connection is still very bad these days, mostly after the earthquake that struck Taiwan last week. Most of ISP still having problem recovering their connection to the normal condition (including my ISP). Luckily my cousin had a Speedy connection, so i can use it and write this post. When the connection is fully recovered, then you can give it a try again :D