Jalan Malioboro is the main shopping strip and always crowded. Batik is the thing to buy -- Mirota Batik on the north side of Beringharjo Market is a reliable one-stop shop for batik cloth, wall hangings, puppets, kris daggers, and other Javanese crafts, with prices from Rp 10,000 for small items up to Rp 200,000 for antiques. Beringharjo Market itself is worth a wander for textiles and spices.
The sidewalk vendors along Malioboro sell miniature guitars, mopeds made from recycled metal, and wooden tricycles -- fun souvenirs at bargain prices if you are willing to haggle.