Forget Jerusalem's old town - if you want to shop in a real market without tourist items, head to Nablus, where what you see on display is what people living there want to buy!
Get lost in the market, discover interesting things and meet lovely people. You may also discover bullet holes and destroyed buildings. This is the result of the Israeli military operations in Nablus during the second Intifada in 2002.
More info on Nablus:
UNESCO application for the Old Town