Enjoying shopping experience, hunting exclusive souvenirs of Jogja, you may walk on foot along the arcades of Malioboro Street. There are many vendors selling their merchandises, ranging from such local handicrafts as batik, rattan ornament, leather puppet, bamboo handicrafts (key holder, ornament lamp, and others) as well as blangkon (Javanese / Jogjanese traditional cap) and silver goods to general little things that you may find in other trading places. Along the arcade, you will not only enjoy shopping peacefully on sunny or rainy days but they also enjoy bargaining prices. If they are good at bargaining and have good luck, they will end up buying at third quarter or even half of the prices offered.
Please make sure that you are not cheated by the offered prices. Usually, the vendors will increase the prices for tourists. But be wise too. Buy if the price make sense to you, cause high price for indonesian probably still very low for you.