Visit the bazaars/markets or souks as they`re known in Arabic.
You`ll find lots to buy in the souks, I did my Christmas shopping in them. Do be prepared to haggle for prices, I was usually able to get the items for about 25 to 30% of what they asked. I especially liked the alabaster bowls and plates that you could buy. Watch out for the quality though.
Be warned that many of the vendors will try and do a switch with your money. Never hand your money over until you have the full amount in your hand. They might try and switch the bills and say you gave them 50 piasters instead of 50 pounds.