I always come to Little Tokyo Market Place at least once a week to take advantage of their weekly specials on produce, meats, seafood, and specialty Asian groceries.  Not only is it much more convenient to my home in DTLA that other Asian supermarkets, but I think the value for the quality of the groceries I get here is superior.  The deli and Sakura Noodle food stall have convenient options for affordable and delicious takeout too when I don't really feel like cooking. 

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