Pasar Beringharjo (Beringharjo Marketplace)
It's on Jalan Pabringan 1, Yogyakarta 55122 (north of Vredeburg Fort), +62 274 515871, 561510. Literally means slanted land, Beringaharjo is the largest traditional marketplace in Yogyakarta. The vendors sell many kind of goods, ranging from basic household items (vegetables, fruits, meats) to many kind of handicrafts. Haggle furiously.
Mirota Batik (opp Pasar Beringharjo)
It's on Jalan Ahmad Yani 9, Yogyakarta 55122, +62 274 588524, 518127, 547016 . The large family-owned store offers plenty of handicrafts, not only from Yogyakarta but also from all part of Indonesia.
Dagadu (lower ground floor Malioboro Mall)
Offers funny contemporary t-shirts and souvenirs that revolves around Yogyakarta people's culture.
Ciamis Art Shop (153 Jl. Malioboro)
Shadow puppets, masks, carvings, and more at fixed prices that are lower than in the market. Open from 9:00 - 13:00 and 18:00 - 21:00.
Nadzar (187 Jl. Malioboro)
Huge souvenir shop specializing in batik, art, jewelry, and more. Has every souvenir you could imagine and all at fixed prices.
If travelling on foot is not your thing, you can ride the pedal-powered trishaw called becak, or the andong horsecart.