A number of local craft stores in Hamadi sell Papuan wood carvings, bark paintings, and other artifacts.
Abepura markets are a large local market in Abepura 20 mins drive from Jayapura city. This market caters to locals and as such does not stock tourist items.
Jayapura city markets seem to be open every night and sell a broad range of items. Although most are for local consumption cheap clothes, accessories, DVDs etc. can be found here. Local produce is also sold at these markets and makes for an interesting walk.