What is the name of food from Yogyakarta?

Answer 1

Here is a few of the most popular dishes:-

Gudeg,
a curry of jackfruit, chicken and egg served with rice, and is the most famous local dish. Goopy slop in various shades of brown, the stuff does not look particularly appetizing, but it can be tasty if done right.

Ayam Goreng Mbok Berek (Mbok Berek's Fried Chicken).
Fried free range chicken with mild garlic and coriander flavor served with crunchy crackers.

Nasi Langgi (Langgi Rice).
Warm rice served with various side dishes.

Kipo,
bite size snacks made of green colored tapioca dough filled with sweetened grated coconut.
.
Bakpia,
another bite size snack made from sweetened greenbean paste wrapped with thin dough pastry. The most popular bakpia is known as Bakpia Patuk,

Jadah Tempe,
sandwich of rice cake and sweet beancake.

Answer 2

Panang (Padang?) When you go to one of these restaurants they start bringing out little plates with all sorts of stuff on them. Some are recognizable, some look like tree bark or offal. You pay for what you eat.

There's usually a sink right in the restaurant to wash your hands before and/or after one of these meals. Interesting concept.