Wayang puppets (a form of the local puppet theatre art) would be a very unusual present. Wayang often depicts mythical creatures, Gods, and heroes. You can also buy a memento copy of the local music instruments like maracas, mbira, drums, and flutes (and these souvenirs are pretty cheap). You can even produce a simple melody with it. However, if clarity of sound is an important aspect for you, then it’s better to look for a real instrument by the local craftsmen.
Another useful stuff you can buy here is leather bags, bracelets, or a pair of shoes. They’re usually made from python or cobra skin. It’s not really expensive, looks quite nice, and they are of good quality. Some travelers prefer to bring local masks or erotic souvenirs from the island. The erotic ones are that popular not just for its provocative look but as they symbolize fertility and prosperity. Above all, you can also buy organic cosmetics here.
Don’t forget to buy a pack or two of coffee, as Indonesia stand on the fourth place in the international coffee production rating. The local sorts are known for its high quality and reasonable price. Or you can buy Jasmine tea, Jasmine honey or chocolate as well. As you do shopping, remember that you do can and must bargain in markets and small shops in order not to pay too much. As you bargain, don’t show how you actually like a product, you can even just leave. If a seller agrees to low the price, he’ll come and catch you up; if not, just look for another seller.