Local markets is the place where you could understand more about the local's food culture. In Yogyakarta, eRayn3 has manage to visit 2 of the well known local market to learn more about the foods they buy and cook.
Each every places local living are different in some way. Whether you are a city person or a village/kampung person in your country, other countries village/kampung or local living wouldn't be the same. When we travel, the best thing to do is to experience the local living. How they lives and what is their culture there. The best place to experience all these would be in their villages/kampung.