This is "real" Alexandria and a real treat too. Unlike the Khan in Cairo, tourists don't get hassled to buy stuff here. As it is not touristy you'd better bring a phrase book if you are looking for something specific, otherwise just enjoy wandering around the streets.
The Eastern end starts with clothes and material (some lovely scarves here), then there are a few streets with spices (far, far cheaper than Cairo!) and then the fresh fish, fruit and vegetables take over.
Best buys are loofas, dried Hibiscus, dates and Halva.
It's relatively easy to find your way home as well; as turning off the main street will take you to the Corniche and a taxi will never be too far away.
Walk inland from the Unknown Soldier memorial on the Corniche (Midan Orabi) until you hit the main crossroads (Midan el-Tahrir). Go right here and you'll gradually walk deeper and deeper into the market. It runs parallel to the Corniche between here and El-Anfushi area, just a few blocks in from the bay.
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