Many people said that you have to try sate klathak if you're in Jogja. Sate klathak is young goat satay.
Tried the one in Jombor area named Sate Klathak Pak Je Je. The satay is very tender and juicy. Luving the gulai/curry sauce!! Soo yummy :)
I also tried their tengkleng. Actually it is goat's marrow bone cooked in spicy herbs called bumbu rica-rica. It is so yummy and spicy. I suggest you to use straw to suck up the marrows inside. Quite a hard work to eat but very worth the flavor inside.
Really recommend these dishes if you're visiting Yogyakarta. The price?? Very affordable and worth the flavor.