1. Music: Riches galore, most of all gamelan music. My favorite CD of the soft, dreamy Javanese gamelan is Javanese Court Gamelan, on Nonesuch. Most gamelan music is from Bali. Golden Rain is one good pick of many, but virtually any gamelan CD without a half-naked woman on the cover will be excellent. Look for the French and Japanese labels in this area. For other areas of Indonesian music, there is a very good Smithsonian set of 20 CDs; the acoustic guitar music is especially interesting. Here is a one-CD sampler from that set.
2. Novel: Pramoedya Toer’s Buru Quartet (four volumes, but quite readable) is perhaps the least read great novel of the 20th century. On the surface it concerns imperialism but it is actually about what a life really consists of and how that life is defined. Reading each volume redefines the one that came before it. Like gamelan music, very highly recommended. The author "wrote" most of it during his 14-year stint in Buru prison, but most of the time without the benefit of pen or paper.
3. Food dish: This is a no brainer, Beef Rendang. In general the food from Sumatra is spicier. Get Sumatran Rijstafel when you can, it is better than Javanese though both are wonderful.
4. Textiles: A rich area, but the subtle colors and textures of Sumatra are tops. The early twentieth century is an especially strong time but the quality continues to be high. Textiles from Timor are not to be overlooked, although of course now they are independent. Here is one Sumatran image. Here is another nice piece. Try this one too.
5. Film: I have never seen an Indonesian movie, though in my defense I have never turned down an opportunity to see one either. Nia Dinata is currently a renowned Indonesian filmmaker. The reasonably good Year of Living Dangerously is the only movie I know set in Indonesia. Can you all help out here?
6. Painter: I like the Naive Art of Bali, so how about Nyoman Lesug? Sadly he is not well represented on the web. Dewa Putu Bedi is perhaps better known. Anak Agung Gede Sobrat is another option. Here are some other names to start with. But it is increasingly difficult to run across the better stuff.
The bottom line: Most people underexplore tthe culture of this region, relative to the quality of their best offerings. I am not yet sure, however, whether we should call it a "country."