There are many opportunities for buying traditional local products and souvenirs.  Here are just a few of your options: 
Markets
 
Fish market Dawei
 
Night fish market at the beach of Pyin Gyi village (2:00 AM – 7:00 AM)
 
Zay Gyi Market (fresh food, dried fish, dry goods, textiles)
 
 
Souvenirs
 
Mali Ngapi (059-2022557), 1087 Shwe Taung Sar Street
 
Dawei Beauty (059-2023987), DDPC Shopping Mall
 
Zay Gyi market (dried fish)
 
MMT (cashew nuts), Mingalar Street
 
Goldshops, around Zay Gyi market
 
 
Shopping Center
DDPC Shopping Mall, intersection of Ko Myaw Kin Street and Seikkan Thar Street
Dawei Beauty Maung Magan
Dawei Beauty Maung Magan

Coconut Guest House
Coconut Guest House

Diamond Crown
Diamond Crown

Dawei Beauty Maung Magan
Dawei Beauty Maung Magan

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